Upper total domination in claw-free graphs

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S (other than itself). The maximum cardinality of a minimal total dominating set of G is the upper total domination number of G, denoted by Gamma(t)(G). We establish bounds on Gamma(t)(G) for claw-free graphs G in terms of the number n of vertices and the minimum degree delta of G. We show that Gamma(t)(G) less than or equal to 2(n + 1)/3 if delta is an element of {1,2}, Gamma(t)(G) less than or equal to 4n/(delta + 3) if delta is an element of {3,4}, and Gamma(t)(G) less than or equal to n/2 if delta greater than or equal to 5. The extremal graphs are characterized. (C) 2003 Wiley Periodicals, Inc.