Cop number of $2K_2$-free graphs

Stephen Testa; Vaidy Sivaraman

Cop number of $2K_2$-free graphs

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arxiv 1903.11484 v1 pith:XV7POXSI submitted 2019-03-27 math.CO cs.DM

Vaidy Sivaraman , Stephen Testa This is my paper · ORCID

classification math.COcs.DM

keywords freenumbergraphconjecturecyclediametereverygraphs

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abstract

We prove that the cop number of a $2K_2$-free graph is at most $2$ if it has diameter $3$ or does not have an induced cycle of length $k$, where $k \ \in \{3,4,5\}$. We conjecture that the cop number of every $2K_2$-free graph is at most $2$.

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Cops and Robbers on Graphs with Path Constraints
math.CO 2025-09 accept novelty 6.0 of 10

Forbidden-subgraph classes of graphs with no long induced path are shown to have cop number at most about k/2 for (P_k,E)-free graphs and at most ceil(2p/3)+3 when the longest path has p vertices.

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