Author

Alexander Clow

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Preprint Oct 2026

Cops and Robbers on Graphs without Long or Short Holes

In 2019, Sivaraman conjectured that every $P_k$-free graph has cop number at most $k-3$ for $k\geq 5$. Chudnovsky, Norin, Seymour, and Turcotte proved $P_5$-free graphs have cop number at most $2$. For $k\geq 6$ Sivaraman's conjecture remains widely open. There is little evidence to believe Sivaraman's conjecture is op...

Alexander Clow · 0 citations

Preprint Jul 2026

MAD Phase Transitions in the Oriented Chromatic Number

For an oriented graph $G$ the oriented chromatic number of $G$, written $\chi_o(G)$, is the least integer $t$ such that $G$ has a homomorphism to a tournament on $t$ vertices. The oriented chromatic number of a simple graph $H$ is the maximum oriented chromatic number over all orientations of $H$. Borodin, Kostochka, N...

Alexander Clow · 0 citations