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

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.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Tobias Müller, Attila Pór, Jean-Sébastien Sereni
• Keywords: Boundary Vertex, Constant Factor, DM 2008, Possible Lower Bound