edge coloring

Stream: graph theory

[Matthew Ballard]

@Utku Okur and Alec Helm worked on some results for edge colorings of graphs for a recent graduate class here. The repo is uofsc-spring-2023-math-768-001/project1. The current state of the repo might make your eyes bleed though.

Since @Yaël Dillies asked about this on another thread, I thought I should at least record here.

[Kevin Buzzard]

Is the repo public? Right now the hashtag isn't resolving to anything (for me)

[Matthew Ballard]

Thanks. Fixed.

[Matthew Ballard]

The goal was to do the two bounds in terms of maximal degree. We got

theorem maxDegree_le_edgeChromaticNumber [Fintype V] [DecidableRel G.Adj] [Fintype (edgeSet G)] :
    maxDegree G ≤ edgeChromaticNumber G

But not the harder direction. I am not sure if Utku or Alec are planning on working on this.