Edge Colouring Multigraphs

Thursday, November 20, 2014 - 2:00pm - 3:00pm
Lind 305
Penny Haxell (University of Waterloo)
The chromatic index of a multigraph G is the smallest k such that the edges of G can be coloured with k colours so that no two edges of the same colour share a vertex. It is easy to see that the chromatic index of G is at least the maximum degree d, and it can be as large as 3d/2.

An old conjecture due to Goldberg and (independently) Seymour essentially states that if a multigraph has chromatic index d+k > d+1 then it must contain a small odd subset S of vertices that induces too many edges to be coloured with d+k colours. This talk will report on recent joint work with Hal Kierstead proving a weakened version of this statement, and describe an important tool for studying edge colourings (the method of Tashkinov trees).