### On the List Coloring Version of Reed's Conjecture

Combinatorics Seminar

9th March 2018, 12:00 pm – 1:00 pm

Howard House, 4th Floor Seminar Room

Reed conjectured in 1998 that the chromatic number of a graph should be at most the average of the clique number (a trivial lower bound) and maximum degree plus one (a trivial upper bound); in support of this conjecture, Reed proved that the chromatic number is at most some nontrivial convex combination of these two quantities. King and Reed later showed that a fraction of roughly 1/130000 away from the upper bound holds. Motivated by a paper by Bruhn and Joos, last year Bonamy, Perrett, and Postle proved for large enough maximum degree, a fraction of 1/26 away from the upper bound holds, a signfi cant step towards the conjectured value of 1/2. Using new techniques, we show that the list-coloring version holds; for large enough maximum degree, a fraction of 1/13 suffices for list chromatic number. This result implies that 1/13 suffices for ordinary chromatic number as well. This is joint work with Luke Postle.

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