#graph-theory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #graph-theory, aggregated by home.social.
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How does graph theory reveal scholarly style?
Freudenberg = sparse, decentralized network. Losev = dense philosophical hub. Meletinskii = uniform academic grid.
Same myth studies, completely different terminological fingerprints.https://nevmenandr.github.io/portfolio/assets/pdf/82517678.pdf
#GraphTheory #DigitalHumanities #Linguistics #NetworkScience #Academia
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How does graph theory reveal scholarly style?
Freudenberg = sparse, decentralized network. Losev = dense philosophical hub. Meletinskii = uniform academic grid.
Same myth studies, completely different terminological fingerprints.https://nevmenandr.github.io/portfolio/assets/pdf/82517678.pdf
#GraphTheory #DigitalHumanities #Linguistics #NetworkScience #Academia
-
How does graph theory reveal scholarly style?
Freudenberg = sparse, decentralized network. Losev = dense philosophical hub. Meletinskii = uniform academic grid.
Same myth studies, completely different terminological fingerprints.https://nevmenandr.github.io/portfolio/assets/pdf/82517678.pdf
#GraphTheory #DigitalHumanities #Linguistics #NetworkScience #Academia
-
How does graph theory reveal scholarly style?
Freudenberg = sparse, decentralized network. Losev = dense philosophical hub. Meletinskii = uniform academic grid.
Same myth studies, completely different terminological fingerprints.https://nevmenandr.github.io/portfolio/assets/pdf/82517678.pdf
#GraphTheory #DigitalHumanities #Linguistics #NetworkScience #Academia
-
How does graph theory reveal scholarly style?
Freudenberg = sparse, decentralized network. Losev = dense philosophical hub. Meletinskii = uniform academic grid.
Same myth studies, completely different terminological fingerprints.https://nevmenandr.github.io/portfolio/assets/pdf/82517678.pdf
#GraphTheory #DigitalHumanities #Linguistics #NetworkScience #Academia
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Alright, future engineers!
**Graph:** A set of nodes (vertices) linked by connections (edges).
Ex: Friends in a social network are nodes, friendships are edges.
Pro-Tip: Use graphs to model relationships & find optimal paths/flows.
#GraphTheory #DiscreteMath #STEM #StudyNotes -
Alright, future engineers!
**Graph:** A set of vertices (nodes) connected by edges.
Ex: Social networks: people are nodes, friendships are edges.
Pro-Tip: Vertices can exist without edges (isolated nodes)!
#GraphTheory #DiscreteMath #STEM #StudyNotes -
k-Coloring is Faster than Computing the Chromatic Number
https://arxiv.org/abs/2607.25973
Comments: https://news.ycombinator.com/item?id=49119508
#HackerNews #kColoring #ChromaticNumber #GraphTheory #Algorithms #Research
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k-Coloring is Faster than Computing the Chromatic Number
https://arxiv.org/abs/2607.25973
Comments: https://news.ycombinator.com/item?id=49119508
#HackerNews #kColoring #ChromaticNumber #GraphTheory #Algorithms #Research
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k-Coloring is Faster than Computing the Chromatic Number
https://arxiv.org/abs/2607.25973
Comments: https://news.ycombinator.com/item?id=49119508
#HackerNews #kColoring #ChromaticNumber #GraphTheory #Algorithms #Research
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k-Coloring is Faster than Computing the Chromatic Number
https://arxiv.org/abs/2607.25973
Comments: https://news.ycombinator.com/item?id=49119508
#HackerNews #kColoring #ChromaticNumber #GraphTheory #Algorithms #Research
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k-Coloring is Faster than Computing the Chromatic Number
https://arxiv.org/abs/2607.25973
Comments: https://news.ycombinator.com/item?id=49119508
#HackerNews #kColoring #ChromaticNumber #GraphTheory #Algorithms #Research
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Ah yes, another prophetic telling of our inevitable AI overlords who will apparently build "cities" while we sleep. 💤 Because clearly, the way to solve world issues is through the power of endless loops and graph theory. Who knew the key to civilization was trapped in your IDE all along? 🤦♂️
https://yegge.ai/essays/the-shape-of-things-to-come/ #AIOverlords #PropheticTales #GraphTheory #CivilizationInCode #EndlessLoops #HackerNews #ngated -
Ah yes, another prophetic telling of our inevitable AI overlords who will apparently build "cities" while we sleep. 💤 Because clearly, the way to solve world issues is through the power of endless loops and graph theory. Who knew the key to civilization was trapped in your IDE all along? 🤦♂️
https://yegge.ai/essays/the-shape-of-things-to-come/ #AIOverlords #PropheticTales #GraphTheory #CivilizationInCode #EndlessLoops #HackerNews #ngated -
Ah yes, another prophetic telling of our inevitable AI overlords who will apparently build "cities" while we sleep. 💤 Because clearly, the way to solve world issues is through the power of endless loops and graph theory. Who knew the key to civilization was trapped in your IDE all along? 🤦♂️
https://yegge.ai/essays/the-shape-of-things-to-come/ #AIOverlords #PropheticTales #GraphTheory #CivilizationInCode #EndlessLoops #HackerNews #ngated -
Ah yes, another prophetic telling of our inevitable AI overlords who will apparently build "cities" while we sleep. 💤 Because clearly, the way to solve world issues is through the power of endless loops and graph theory. Who knew the key to civilization was trapped in your IDE all along? 🤦♂️
https://yegge.ai/essays/the-shape-of-things-to-come/ #AIOverlords #PropheticTales #GraphTheory #CivilizationInCode #EndlessLoops #HackerNews #ngated -
Ah yes, another prophetic telling of our inevitable AI overlords who will apparently build "cities" while we sleep. 💤 Because clearly, the way to solve world issues is through the power of endless loops and graph theory. Who knew the key to civilization was trapped in your IDE all along? 🤦♂️
https://yegge.ai/essays/the-shape-of-things-to-come/ #AIOverlords #PropheticTales #GraphTheory #CivilizationInCode #EndlessLoops #HackerNews #ngated -
Border crossing distances by Bellman-Ford
#graphtheory #computerscience #math -
Release 0.3.2 of #Higraph is out.
Edge names can be placed anywhere along the edge, and will maintain their position. And a handful of bugs/ rough edges rubbed off.I am singularly pleased with the edge name code - it uses the spline parameter t, and a perpendicular distance d, to convert between the (x,y) screen coords and (t,d), which are "natural" coords for a spline.
Find it here:
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Release 0.3.2 of #Higraph is out.
Edge names can be placed anywhere along the edge, and will maintain their position. And a handful of bugs/ rough edges rubbed off.I am singularly pleased with the edge name code - it uses the spline parameter t, and a perpendicular distance d, to convert between the (x,y) screen coords and (t,d), which are "natural" coords for a spline.
Find it here:
-
Release 0.3.2 of #Higraph is out.
Edge names can be placed anywhere along the edge, and will maintain their position. And a handful of bugs/ rough edges rubbed off.I am singularly pleased with the edge name code - it uses the spline parameter t, and a perpendicular distance d, to convert between the (x,y) screen coords and (t,d), which are "natural" coords for a spline.
Find it here:
-
Release 0.3.2 of #Higraph is out.
Edge names can be placed anywhere along the edge, and will maintain their position. And a handful of bugs/ rough edges rubbed off.I am singularly pleased with the edge name code - it uses the spline parameter t, and a perpendicular distance d, to convert between the (x,y) screen coords and (t,d), which are "natural" coords for a spline.
Find it here:
-
Release 0.3.2 of #Higraph is out.
Edge names can be placed anywhere along the edge, and will maintain their position. And a handful of bugs/ rough edges rubbed off.I am singularly pleased with the edge name code - it uses the spline parameter t, and a perpendicular distance d, to convert between the (x,y) screen coords and (t,d), which are "natural" coords for a spline.
Find it here:
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A series of papers by Chun-Hung Liu [https://people.tamu.edu/~chliu/] and I have finally all been accepted for publication. The topic is clustered graph colouring. Here one relaxes the requirement that adjacent vertices are assigned distinct colours. Instead, each monochromatic component has bounded size. The goal is to minimise the number of colours. The theme of these papers is that for graphs excluding a complete bipartite subgraph \(K_{s,t}\) with \(s\leq t\) and with some other structural property, the number of colours in a clustered colouring only depends on \(s\), and is in fact only \(s\) plus a small constant. The structural properties considered are bounded treewidth, bounded layered treewidth, excluding a minor, or excluding an odd minor. All the dependence on the excluded structural property is in the size of the monochromatic components.
• Clustered graph coloring and layered treewidth. J. Combinatorics, accepted 2026 (arXix:1905.08969).
• Clustered coloring of graphs excluding a subgraph and a minor, J. Combinatorial Theory Series B 181:95–139, 2026 (arXiv:1905.09495).
• Clustered variants of Hajós’ conjecture, J. Combinatorial Theory Series B 152:27–54, 2022 (arXix:1908.05597).
• Clustered coloring of graphs with bounded layered treewidth and bounded degree, European J. Combinatorics 122:103730, 2024 (arXix:2209.12327). -
A series of papers by Chun-Hung Liu [https://people.tamu.edu/~chliu/] and I have finally all been accepted for publication. The topic is clustered graph colouring. Here one relaxes the requirement that adjacent vertices are assigned distinct colours. Instead, each monochromatic component has bounded size. The goal is to minimise the number of colours. The theme of these papers is that for graphs excluding a complete bipartite subgraph \(K_{s,t}\) with \(s\leq t\) and with some other structural property, the number of colours in a clustered colouring only depends on \(s\), and is in fact only \(s\) plus a small constant. The structural properties considered are bounded treewidth, bounded layered treewidth, excluding a minor, or excluding an odd minor. All the dependence on the excluded structural property is in the size of the monochromatic components.
• Clustered graph coloring and layered treewidth. J. Combinatorics, accepted 2026 (arXix:1905.08969).
• Clustered coloring of graphs excluding a subgraph and a minor, J. Combinatorial Theory Series B 181:95–139, 2026 (arXiv:1905.09495).
• Clustered variants of Hajós’ conjecture, J. Combinatorial Theory Series B 152:27–54, 2022 (arXix:1908.05597).
• Clustered coloring of graphs with bounded layered treewidth and bounded degree, European J. Combinatorics 122:103730, 2024 (arXix:2209.12327). -
I have a new paper “Optimal tree-decompositions with bags of bounded pathwidth” with Kevin Hendrey, Robert Hickingbotham and Jędrzej Hodor [https://arxiv.org/abs/2607.27601] We show that every planar graph has a tree-decomposition with optimal width such that the subgraph induced by each bag has pathwidth at most 3. This was previously known with `pathwidth' replaced by the weaker notion of `treewidth'. Moreover, the union of any k bags has pathwidth O(k). The first result generalises for graphs embeddable on any fixed surface, and other settings. As a byproduct, we give a new proof of the linear grid minor theorem for planar graphs by Robertson, Seymour and Thomas.
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I have a new paper “Optimal tree-decompositions with bags of bounded pathwidth” with Kevin Hendrey, Robert Hickingbotham and Jędrzej Hodor [https://arxiv.org/abs/2607.27601] We show that every planar graph has a tree-decomposition with optimal width such that the subgraph induced by each bag has pathwidth at most 3. This was previously known with `pathwidth' replaced by the weaker notion of `treewidth'. Moreover, the union of any k bags has pathwidth O(k). The first result generalises for graphs embeddable on any fixed surface, and other settings. As a byproduct, we give a new proof of the linear grid minor theorem for planar graphs by Robertson, Seymour and Thomas.
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I recommend Richard Montgomery's excellent survey “Recent progress in graph theory using expansion” [https://arxiv.org/pdf/2607.26049].
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I recommend Richard Montgomery's excellent survey “Recent progress in graph theory using expansion” [https://arxiv.org/pdf/2607.26049].
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But try telling that to Cytoscape Web:
web.cytoscape.org/ff1f5d20-221...
#math #computerscience #graphtheory -
A train leaves the station (bottom) heading west. Can it return to the station heading east?
Is there anywhere the train might get stuck?
Is there anywhere the train can reach but only from one direction?
I call this directed node networks.
#mathsky
#graphtheory
#math4kids -
Question for #Mathstodon
When you *draw* a graph (or a graph-like thing) on a computer, either for your own thinking, or for a paper/ formal communication, what do you use?
I am not a #GraphTheory person, so I'm sure I'm missing some - please let me know in the comments.
Boosts are welcome. -
Question for #Mathstodon
When you *draw* a graph (or a graph-like thing) on a computer, either for your own thinking, or for a paper/ formal communication, what do you use?
I am not a #GraphTheory person, so I'm sure I'm missing some - please let me know in the comments.
Boosts are welcome. -
Question for #Mathstodon
When you *draw* a graph (or a graph-like thing) on a computer, either for your own thinking, or for a paper/ formal communication, what do you use?
I am not a #GraphTheory person, so I'm sure I'm missing some - please let me know in the comments.
Boosts are welcome. -
Question for #Mathstodon
When you *draw* a graph (or a graph-like thing) on a computer, either for your own thinking, or for a paper/ formal communication, what do you use?
I am not a #GraphTheory person, so I'm sure I'm missing some - please let me know in the comments.
Boosts are welcome. -
Question for #Mathstodon
When you *draw* a graph (or a graph-like thing) on a computer, either for your own thinking, or for a paper/ formal communication, what do you use?
I am not a #GraphTheory person, so I'm sure I'm missing some - please let me know in the comments.
Boosts are welcome. -
Alright, future engineers!
**Path (Graph Theory):** A sequence of distinct vertices connected by edges.
Ex: In a network diagram, A-B-C is a path from A to C.
Pro-Tip: If a path starts & ends at the same vertex, it's called a cycle!
#GraphTheory #DiscreteMath #STEM #StudyNotes -
Learn why the Floyd-Warshall algorithm does not assume paths of three edges and how dynamic programming finds shortest paths of any length. https://hackernoon.com/floyd-warshall-algorithm-handling-paths-longer-than-three-edges-without-fixed-maximum-length-assump #graphtheory
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Learn why the Floyd-Warshall algorithm does not assume paths of three edges and how dynamic programming finds shortest paths of any length. https://hackernoon.com/floyd-warshall-algorithm-handling-paths-longer-than-three-edges-without-fixed-maximum-length-assump #graphtheory
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Learn why the Floyd-Warshall algorithm does not assume paths of three edges and how dynamic programming finds shortest paths of any length. https://hackernoon.com/floyd-warshall-algorithm-handling-paths-longer-than-three-edges-without-fixed-maximum-length-assump #graphtheory
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Learn why the Floyd-Warshall algorithm does not assume paths of three edges and how dynamic programming finds shortest paths of any length. https://hackernoon.com/floyd-warshall-algorithm-handling-paths-longer-than-three-edges-without-fixed-maximum-length-assump #graphtheory
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Learn why the Floyd-Warshall algorithm does not assume paths of three edges and how dynamic programming finds shortest paths of any length. https://hackernoon.com/floyd-warshall-algorithm-handling-paths-longer-than-three-edges-without-fixed-maximum-length-assump #graphtheory
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The #paperOfTheDay is "The Ehrhart polynomial of a matroid specializes to the beta invariant" from 2025.
A #matroid is an abstract generalization of a set of vectors in a vector space: Consider some set of k vectors in R^n (allowing k>n). Some of these k vectors could be linearly independent, but assume that not all of them are. If some subset is linearly independent, then so is every subset of that subset. This and a few other properties jointly give the definition of a matroid: Basically, consider the same logical relations arising from linear independence, but without demanding that the objects under consideration are actually vectors in R^n.
If one declares the elements of a matroid to be unit vectors in some abstract vector space (these basis vectors are all linearly independent in that abstract space, whereass not all elements are independent in the matroid), then the maximum set of independent vectors in the matroid amounts to some subset of these abstract vectors, whose convex hull is a polytope. This polytope contains a finite number of points of Z^n. If one rescales the polytope by an integer t, the number of lattice points changes. It turns out that the number of lattice points included is a polynomial of t (not a more complicated function), this defines the Ehrhart polynomial.
Every graph gives rise to a matroid (but not every matroid can be represented as a graph). For graphs, the Tutte polynomial is a classical quantity. The linear term of the Tutte polynomial is the Crapo-beta invariant (and can also be defined for non-graphical matroids). The present paper proves that a linear term of the Ehrhart polynomial coincides with beta. https://arxiv.org/abs/2504.15518 #mathematics #graphTheory -
The #paperOfTheDay is "The Ehrhart polynomial of a matroid specializes to the beta invariant" from 2025.
A #matroid is an abstract generalization of a set of vectors in a vector space: Consider some set of k vectors in R^n (allowing k>n). Some of these k vectors could be linearly independent, but assume that not all of them are. If some subset is linearly independent, then so is every subset of that subset. This and a few other properties jointly give the definition of a matroid: Basically, consider the same logical relations arising from linear independence, but without demanding that the objects under consideration are actually vectors in R^n.
If one declares the elements of a matroid to be unit vectors in some abstract vector space (these basis vectors are all linearly independent in that abstract space, whereass not all elements are independent in the matroid), then the maximum set of independent vectors in the matroid amounts to some subset of these abstract vectors, whose convex hull is a polytope. This polytope contains a finite number of points of Z^n. If one rescales the polytope by an integer t, the number of lattice points changes. It turns out that the number of lattice points included is a polynomial of t (not a more complicated function), this defines the Ehrhart polynomial.
Every graph gives rise to a matroid (but not every matroid can be represented as a graph). For graphs, the Tutte polynomial is a classical quantity. The linear term of the Tutte polynomial is the Crapo-beta invariant (and can also be defined for non-graphical matroids). The present paper proves that a linear term of the Ehrhart polynomial coincides with beta. https://arxiv.org/abs/2504.15518 #mathematics #graphTheory -
The #paperOfTheDay is "The Ehrhart polynomial of a matroid specializes to the beta invariant" from 2025.
A #matroid is an abstract generalization of a set of vectors in a vector space: Consider some set of k vectors in R^n (allowing k>n). Some of these k vectors could be linearly independent, but assume that not all of them are. If some subset is linearly independent, then so is every subset of that subset. This and a few other properties jointly give the definition of a matroid: Basically, consider the same logical relations arising from linear independence, but without demanding that the objects under consideration are actually vectors in R^n.
If one declares the elements of a matroid to be unit vectors in some abstract vector space (these basis vectors are all linearly independent in that abstract space, whereass not all elements are independent in the matroid), then the maximum set of independent vectors in the matroid amounts to some subset of these abstract vectors, whose convex hull is a polytope. This polytope contains a finite number of points of Z^n. If one rescales the polytope by an integer t, the number of lattice points changes. It turns out that the number of lattice points included is a polynomial of t (not a more complicated function), this defines the Ehrhart polynomial.
Every graph gives rise to a matroid (but not every matroid can be represented as a graph). For graphs, the Tutte polynomial is a classical quantity. The linear term of the Tutte polynomial is the Crapo-beta invariant (and can also be defined for non-graphical matroids). The present paper proves that a linear term of the Ehrhart polynomial coincides with beta. https://arxiv.org/abs/2504.15518 #mathematics #graphTheory -
The #paperOfTheDay is "The Ehrhart polynomial of a matroid specializes to the beta invariant" from 2025.
A #matroid is an abstract generalization of a set of vectors in a vector space: Consider some set of k vectors in R^n (allowing k>n). Some of these k vectors could be linearly independent, but assume that not all of them are. If some subset is linearly independent, then so is every subset of that subset. This and a few other properties jointly give the definition of a matroid: Basically, consider the same logical relations arising from linear independence, but without demanding that the objects under consideration are actually vectors in R^n.
If one declares the elements of a matroid to be unit vectors in some abstract vector space (these basis vectors are all linearly independent in that abstract space, whereass not all elements are independent in the matroid), then the maximum set of independent vectors in the matroid amounts to some subset of these abstract vectors, whose convex hull is a polytope. This polytope contains a finite number of points of Z^n. If one rescales the polytope by an integer t, the number of lattice points changes. It turns out that the number of lattice points included is a polynomial of t (not a more complicated function), this defines the Ehrhart polynomial.
Every graph gives rise to a matroid (but not every matroid can be represented as a graph). For graphs, the Tutte polynomial is a classical quantity. The linear term of the Tutte polynomial is the Crapo-beta invariant (and can also be defined for non-graphical matroids). The present paper proves that a linear term of the Ehrhart polynomial coincides with beta. https://arxiv.org/abs/2504.15518 #mathematics #graphTheory -
The #paperOfTheDay is "The Ehrhart polynomial of a matroid specializes to the beta invariant" from 2025.
A #matroid is an abstract generalization of a set of vectors in a vector space: Consider some set of k vectors in R^n (allowing k>n). Some of these k vectors could be linearly independent, but assume that not all of them are. If some subset is linearly independent, then so is every subset of that subset. This and a few other properties jointly give the definition of a matroid: Basically, consider the same logical relations arising from linear independence, but without demanding that the objects under consideration are actually vectors in R^n.
If one declares the elements of a matroid to be unit vectors in some abstract vector space (these basis vectors are all linearly independent in that abstract space, whereass not all elements are independent in the matroid), then the maximum set of independent vectors in the matroid amounts to some subset of these abstract vectors, whose convex hull is a polytope. This polytope contains a finite number of points of Z^n. If one rescales the polytope by an integer t, the number of lattice points changes. It turns out that the number of lattice points included is a polynomial of t (not a more complicated function), this defines the Ehrhart polynomial.
Every graph gives rise to a matroid (but not every matroid can be represented as a graph). For graphs, the Tutte polynomial is a classical quantity. The linear term of the Tutte polynomial is the Crapo-beta invariant (and can also be defined for non-graphical matroids). The present paper proves that a linear term of the Ehrhart polynomial coincides with beta. https://arxiv.org/abs/2504.15518 #mathematics #graphTheory -
#Higraph progress! The text names of items now open in an in-picture editor as you create the item, and for nodes and blobs, can be moved! This is the last major thing before MVP!
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#Higraph progress! The text names of items now open in an in-picture editor as you create the item, and for nodes and blobs, can be moved! This is the last major thing before MVP!
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#Higraph progress! The text names of items now open in an in-picture editor as you create the item, and for nodes and blobs, can be moved! This is the last major thing before MVP!
-
#Higraph progress! The text names of items now open in an in-picture editor as you create the item, and for nodes and blobs, can be moved! This is the last major thing before MVP!
-
#Higraph progress! The text names of items now open in an in-picture editor as you create the item, and for nodes and blobs, can be moved! This is the last major thing before MVP!
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🧙♂️💡 Oh, joy—another attempt to make math "fun" with a Dungeons & Dragons twist! Because nothing says "rigorous proof" like rolling a 20-sided die while pretending your graph theory is a goblin. 🎲📜
https://dhilst.github.io/algae/game/index.html #mathfun #DungeonsAndDragons #gamification #graphtheory #storytelling #HackerNews #ngated -
🧙♂️💡 Oh, joy—another attempt to make math "fun" with a Dungeons & Dragons twist! Because nothing says "rigorous proof" like rolling a 20-sided die while pretending your graph theory is a goblin. 🎲📜
https://dhilst.github.io/algae/game/index.html #mathfun #DungeonsAndDragons #gamification #graphtheory #storytelling #HackerNews #ngated
