On 02.06.2011 at 12:20 in S11, there is the following noon lecture:
Steinberg's conjecture for higher surfaces
In this talk, we will describe work related to a conjecture of Steinberg, which states that if a planar graph excludes 4-cycles and 5-cycles, then it is 3-colorable. Our work aims to give baseline results for graphs on higher surfaces. In particular, we show that if G is drawn in surface S, is 4-critical and has no cycles of length four through ten, then the number of vertices in G is at most a constant times the Euler genus of S, where c is an explicit constant that comes out of the proof. This is joint work with Robin Thomas.
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