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Article Dans Une Revue Discrete Mathematics Année : 2008

Lower bounding the boundary of a graph in terms of its maximum or minimum degree

Résumé

A vertex v of a graph G is a boundary vertex if there exists a vertex u such that the distance in G from u to v is at least the distance from u to any neighbour of v. We give the best possible lower bound, up to a constant factor, on the number of boundary vertices of a graph in terms of its minimum degree (or maximum degree). This settles a problem introduced by Hasegawa and Saito.
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Dates et versions

hal-00487300 , version 1 (28-05-2010)

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Tobias Müller, Attila Pór, Jean-Sébastien Sereni. Lower bounding the boundary of a graph in terms of its maximum or minimum degree. Discrete Mathematics, 2008, 308 (24), pp.6581--6583. ⟨10.1016/j.disc.2007.12.038⟩. ⟨hal-00487300⟩
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