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arXiv · 1402.2969

Subgraphs and Colourability of Locatable Graphs

Richard A. B. Johnson·Sebastian Koch
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Abstract

We study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked whether there exists a characterisation of the graph property of locatable graphs by either forbidden or forbidden induced subgraphs, both of which we answer in the negative. We then proceed to show that such a characterisation does exist for graphs of diameter at most 2, stating it explicitly, and note that this is not true for higher diameter. Exploring a different direction of topic, we also start research in the direction of colourability of locatable graphs, we also show that every locatable graph is 4-colourable, but not necessarily 3-colourable.

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BibTeXRIS

Richard A. B. Johnson, Sebastian Koch. 2014-02-12. Subgraphs and Colourability of Locatable Graphs. https://arxiv.org/abs/1402.2969

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