Author

Shen-Wei Huang

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Preprint Nov 2026

The Erd\H{o}s--Hajnal property for paths

The well-known Erd\H{o}s-Hajnal conjecture states that for any graph $H$, there is a constant $c=c(H)>0$ such that every $n$-vertex graph $G$ with no induced copies of $H$ contains a clique or an independent set of size at least $n^{c}$. In this paper, we prove that the Erd\H{o}s-Hajnal conjecture holds for every path.

Shen-Wei Huang, Yi-Dong Zhou, Yuwen Zhou · 0 citations

Preprint Oct 2026

A quasi-polynomial $\chi$-bound for $P_6$-free graphs

In this paper we prove that every graph $G$ with no induced six-vertex path satisfies $\chi(G)\le \omega(G)^{c\log_2\omega(G)}$ for $c=45/\log_2(4/3)<109$. The best previous bound was exponential in $\omega(G)$. Our result is the first quasi-polynomial bound for $P_6$-free graphs and generalizes the bound for $P_5$-fre...

Shen-Wei Huang, Yi-Dong Zhou, Yuwen Zhou · 0 citations