Tough spiders

Abstract

Spider graphs are the intersection graphs of subtrees of subdivisions of stars. Thus, spider graphs are chordal graphs that form a common superclass of interval and split graphs. Motivated by previous results on the existence of Hamilton cycles in interval, split and chordal graphs, we show that every 3/2-tough spider graph is hamiltonian. The obtained bound is best possible since there are (3/2 – ε)-tough spider graphs that do not contain a Hamilton cycle. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 23–40, 2007