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Perfect divisibility and perfect-Pollyanna in bull-free graphs

arXiv:2603.21538v2 Announce Type: replace-cross Abstract: A graph $G$ is {\em perfectly divisible} if, for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\omega(H[B])<\omega(H)$. A {\em bull} is a graph consisting of a triangle with two disjoint pendant edges. Ho\`ang [Discrete Math. 349 (2026) 114809] proposed four conjectures: 1.

arXiv CS 1d ago