Cops and robbers on \(2K_2\)-free graphs

We prove that the cop number of any \(2K_2\)-free graph is at most 2, proving a conjecture of Sivaraman and Testa. We also show that the upper bound of \(3\) on the cop number of \(2K_1+K_2\)-free (co-diamond--free) graphs is best possible.

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Turcotte, Jérémie
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.10.2021
Subjects
Diamonds
Graphs
Upper bounds
Online AccessGet full text

Cover

More Information
Summary:We prove that the cop number of any \(2K_2\)-free graph is at most 2, proving a conjecture of Sivaraman and Testa. We also show that the upper bound of \(3\) on the cop number of \(2K_1+K_2\)-free (co-diamond--free) graphs is best possible.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.03124