Some remarks on domination

Abstract

Abstract We prove a conjecture of Favaron et al. that every graph of order n and minimum degree at least three has a total dominating set of size at least n /2. We also present several related results about: (1) extentions to graphs of minimum degree two, (2) examining graphs where the bound is tight, and (3) a type of bipartite domination and its relation to transversals in hypergraphs. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 207–210, 2004