Discussiones Mathematicae Graph Theory 30(4) (2010)
591-609
DOI: https://doi.org/10.7151/dmgt.1516
ON THE EXISTENCE OF A CYCLE OF LENGTH AT LEAST 7 IN A (1, 2)-TWIN-FREE GRAPH
David Auger, Irène Charon, Olivier Hudry
Institut Telecom - Telecom ParisTech & Centre National | Antoine Lobstein
Centre National de la Recherche Scientifique - LTCI UMR 5141
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Abstract
We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.Keywords: undirected graph, twin subsets, identifiable graph, distinguishable graph, identifying code, maximum length cycle.
2010 Mathematics Subject Classification: 05C38, 05C75.
References
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Received 27 July 2009
Revised 14 December 2009
Accepted 14 December 2009
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