AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We show that the associahedron $\mathcal{A}_n$ has chromatic number $O(\log\log n)$, improving on the previously best known upper bound of $O(\log n)$.
Let $P_t$ denote the induced path on $t$ vertices. Let $\omega(G)$ denote the maximum number of vertices in a clique of a graph $G$. Gy\'arf\'as (1987) proved that every $P_t$-free graph $G$ satisfies $\chi(G)\le(t-1)^{\omega(G)-1}$, and Gravier, Ho\`ang, and Maffray (2003) improved this to $\chi(G)\le (t-2)^{\omega(G)...
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