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Jun Gao, Number of (k-1)-cliques in k-critical graph
Tuesday, August 30, 2022 @ 4:30 PM - 5:30 PM KST
Room B332, IBS (기초과학연구원)
We prove that for $n>k\geq 3$, if $G$ is an $n$-vertex graph with chromatic number $k$ but any its proper subgraph has smaller chromatic number, then $G$ contains at most $n-k+3$ copies of cliques of size $k-1$. This answers a problem of Abbott and Zhou and provides a tight bound on a conjecture of Gallai.
This is joint work with Jie Ma.