Emergent Mind
Separating polynomial $χ$-boundedness from $χ$-boundedness
(2201.08814)
Published Jan 21, 2022
in
math.CO
and
cs.DM
Abstract
Extending the idea from the paper by Carbonero, Hompe, Moore, and Spirkl, for every function $f\colon\mathbb{N}\to\mathbb{N}\cup{\infty}$ with $f(1)=1$ and $f(n)\geq\binom{3n+1}{3}$, we construct a hereditary class of graphs $\mathcal{G}$ such that the maximum chromatic number of a graph in $\mathcal{G}$ with clique number $n$ is equal to $f(n)$ for every $n\in\mathbb{N}$. In particular, we prove that there exist hereditary classes of graphs that are $\chi$-bounded but not polynomially $\chi$-bounded.
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