Cop number of graphs without long holes
Combinatorics
2020-01-03 v1 Discrete Mathematics
Abstract
A hole in a graph is an induced cycle of length at least 4. We give a simple winning strategy for t-3 cops to capture a robber in the game of cops and robbers played in a graph that does not contain a hole of length at least t. This strengthens a theorem of Joret-Kaminski-Theis, who proved that t-2 cops have a winning strategy in such graphs. As a consequence of our bound, we also give an inequality relating the cop number and the Dilworth number of a graph.
Cite
@article{arxiv.2001.00477,
title = {Cop number of graphs without long holes},
author = {Vaidy Sivaraman},
journal= {arXiv preprint arXiv:2001.00477},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1903.01338