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arXiv · 1812.06230

Cops and Robbers on Graphs with a Set of Forbidden Induced Subgraphs

Masood Masjoody·Ladislav Stacho
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Abstract

It is known that the class of all graphs not containing a graph $H$ as an induced subgraph is cop-bounded if and only if $H$ is a forest whose every component is a path. In this study, we characterize all sets $\mathscr{H}$ of graphs with some $k\in \mathbb{N}$ bounding the diameter of members of $\mathscr{H}$ from above, such that $\mathscr{H}$-free graphs, i.e. graphs with no member of $\mathscr{H}$ as an induced subgraph, are cop-bounded. This, in particular, gives a characterization of cop-bounded classes of graphs defined by a finite set of connected graphs as forbidden induced subgraphs. Furthermore, we extend our characterization to the case of cop-bounded classes of graphs defined by a set $\mathscr{H}$ of forbidden graphs such that there is $k\in\mathbb{N}$ bounding the diameter of components of members of $\mathscr{H}$ from above.

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Masood Masjoody, Ladislav Stacho. 2018-12-15. Cops and Robbers on Graphs with a Set of Forbidden Induced Subgraphs. https://doi.org/10.1016/j.tcs.2020.06.032

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