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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20220210T163000
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UID:5183-1644510600-1644514200@dimag.ibs.re.kr
SUMMARY:James Davies\, Separating polynomial $\chi$-boundedness from $\chi$-boundedness
DESCRIPTION:We prove that there is a function $f : \mathbb{N} \to \mathbb{N}$ such that for every function $g : \mathbb{N} \to \mathbb{N} \cup \{\infty\}$ with $g(1)=1$ and $g \ge f$\, there is a hereditary class of graphs $\mathcal{G}$ such that for each $\omega \in \mathbb{N}$\, the maximum chromatic number of a graph in $\mathcal{G}$ with clique number $\omega$ is equal to $g(\omega)$. This extends a recent breakthrough of Carbonero\, Hompe\, Moore\, and Spirk. In particular\, this proves that there are hereditary classes of graphs that are $\chi$-bounded but not polynomially $\chi$-bounded. \nJoint work with Marcin Briański and Bartosz Walczak.
URL:https://dimag.ibs.re.kr/event/2022-02-10/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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