Mastodawn

@zbMATH Photo of a "local authors" corner in our department display case!

Prof. Beineke gave a talk about "Milestones" this morning at the Midwest Graph Theory (MIGHTY) LXV conference at Ball State!
https://sites.bsu.edu/mighty/upcoming-mighty-conference/
#PurdueFortWayne #GraphTheory

kipriyanovich 6d ago

Alright, future engineers!
The **Degree of a Vertex** in a graph is the count of edges connected to it. Ex: If `v` is a person, `deg(v)` is their number of friends. Pro-Tip: The sum of all degrees in any graph is always twice the number of edges!
#GraphTheory #DiscreteMath #STEM #StudyNotes

Show thread

Grant_H 6d ago

You asked, and here it is: #hyperedges are basically working. 1200 lines of code & changes in 2 weeks - about 50 odd hours of coding. This was not trivial, but hyperedges are a thing.

There are still some features to add (deletion, XML serialisation), and bugs to squash, but the hard work is done.
😁

#Python #Higraph #GraphTheory #PYside6

#BaconNumber #KevinBacon
#ErdösNumber #erdosnumber #PaulErdös
#FrigyedKarinthy #StanleyMilgram
#SixDegrees #SixDegreesOfSeperation
#GraphTheory

kipriyanovich Apr 9

Alright, future engineers!

A **Tree** is an undirected graph where any two vertices are connected by exactly one path (no cycles). Ex: A graph with N vertices & N-1 edges (no cycles) is a tree. Pro-Tip: Perfect for modeling hierarchical structures like file systems!

#GraphTheory #DataStructures #STEM #StudyNotes

Charo del Genio Apr 2

New paper, with Kirill Kovalenko, Gonzalo Contreras, Stefano Boccaletti and Rubén Sánchez.

People have noticed that, in higher-order networks, synchronization is often explosive, and that cluster synchronization happens very rarely, if ever. We explain why, by showing that symultaneous dynamical equitability across layers or interaction orders is necessary and sufficient for cluster synchronization, except if the coupling functions depend linearly on each other. Since the probability of randomly satisfying this condition is exceedingly low, cluster synchronization is precluded in such networks.

https://www.nature.com/articles/s42005-026-02543-5

#mathematics #physics #science #networks #complexity #HigherOrderNetworks #MultiplexNetworks #synchronization #dynamicalsystems #graphs #graphtheory #equitability #ClusterSynchronization #ExplosiveSynchronization

Grant_H Mar 31

This image is of a simulation of a simple directed #hypergraph , but using an n-ary line rather than a set for the #hyperedge

I have written a working #graphTheory editor for binary edges, where nodes are extended to sets (a #Higraph) , and am contemplating the complexity of n-ary edges with increasing apprehension. It requires refactoring just about the entire edge drawing codebase - 100's of changes across ~2000 lines of #Python.
Is it worth it? Please comment/ vote in the poll below

kipriyanovich Mar 29

Vertex Degree: The number of edges connected to a vertex in a graph. Ex: In a social network, your degree is how many friends you have. Pro-Tip: Sum of all degrees is always 2 * (num of edges) – the Handshaking Lemma!

#GraphTheory #DiscreteMath #STEM #StudyNotes

Ross Kang Mar 23

https://arxiv.org/abs/2603.12358

Here is the *third* manuscript coming out of the "Topics in Ramsey theory" online-only problem-solving session (https://sparse-graphs.mimuw.edu.pl/doku.php?id=sessions:2025sessions:2025session1) of the Sparse (Graphs) Coalition, which took place less than a year ago.

It is still surprising to realise what one can make of such events, if they are set up well.

#combinatorics #remoteconferences #graphtheory #extremalcombinatorics #openscience

Ordered Ramsey and Turán numbers of alternating paths and their variants

An ordered graph is a graph whose vertex set is equipped with a total order. The ordered complete graph $K_N^<$ is the complete graph with vertex set $[N]$ equipped with the natural ordering of the integers. Given an ordered graph $H$, the ordered Ramsey number $R_<(H)$ is the smallest integer $N$ such that every red/blue edge-colouring of $K_N^<$ contains a monochromatic copy of $H$ with vertices appearing in the same relative order as in $H$. Balko, Cibulka, Král, and Kyn\v cl asked whether, among all ordered paths on $n$ vertices, the ordered Ramsey number is minimised by the alternating path $\mathrm{AP}_n$ -- the ordered path with vertex set $[n]$ such that the vertices encountered along the path are $1, n, 2, n - 1,3, n-2,\dots$. Motivated by this problem, we make progress on establishing the value of $R_<(\mathrm{AP}_n)$ by proving that \[ R_{<}(\mathrm{AP}_n)\leq \left(2+\frac{\sqrt{2}}{2}+o(1)\right)n. \] We then use similar methods to determine the exact ordered Turán number of $\mathrm{AP}_n$, and study the ordered Ramsey and Turán numbers of several related ordered paths.

arXiv.org

Linotype Pilgrim Mar 23

#graphtheory #math