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- W3179045793 abstract "A conjecture of Alon, Krivelevich, and Sudakov states that, for any graph $F$, there is a constant $c_F > 0$ such that if $G$ is an $F$-free graph of maximum degree $Delta$, then $chi(G) leq c_F Delta / logDelta$. Alon, Krivelevich, and Sudakov verified this conjecture for a class of graphs $F$ that includes all bipartite graphs. Moreover, it follows from recent work by Davies, Kang, Pirot, and Sereni that if $G$ is $K_{t,t}$-free, then $chi(G) leq (t + o(1)) Delta / logDelta$ as $Delta to infty$. We improve this bound to $(1+o(1)) Delta/log Delta$, making the constant factor independent of $t$. We further extend our result to the DP-coloring setting (also known as correspondence coloring), introduced by Dvořak and Postle." @default.
- W3179045793 created "2021-07-19" @default.
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- W3179045793 date "2021-07-12" @default.
- W3179045793 modified "2023-09-27" @default.
- W3179045793 title "Coloring graphs with forbidden bipartite subgraphs." @default.
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