##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Prof. Michael Molloy

#### University of Toronto

## An improved bound for the List Colouring Conjecture

##### Abstract:

The List Colouring Conjecture posits that the list edge chromatic number of any graph is equal to the edge chromatic number, and thus is at most D+1 where D is the maximum degree. This means that if each edge is assigned a list of $D+1$ colours then it is always possible to obtain a proper edge colouring by choosing one colour from each list.

In the 1990's, Khan proved that one can always obtain a proper edge colouring from lists of size $D+o(D)$, then Molloy and Reed obtained $D+D^{1/2}\mathrm{poly}(\log D)$. We improve that bound to $D+D^{2/5}\mathrm{poly}(\log D)$

Host: Lutz Warnke

### May 21, 2024

### 2:00 PM

APM 7321

Research Areas

Combinatorics****************************