Domination numbers of planar graphs

Abstract

Translate Article

The problem of determining the domination number of a graph is a well known NP-hard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that the domination number of such a graph can be determined in polynomial time. We also give examples of planar graphs of diameter four, and nonplanar graphs of diameter two, having arbitrarily large domination numbers. © 1996 John Wiley & Sons, Inc.