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Forbidden Induced Subgraphs for Toughness



Let math formula be a family of connected graphs. A graph G is said to be math formula-free if G is H-free for every graph H in math formula. We study the relation between forbidden subgraphs in a connected graph G and the resulting toughness of G. In particular, we consider the problem of characterizing the graph families math formula such that every large enough connected math formula-free graph is t-tough. In this article, we solve this problem for every real positive number t. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 191–202, 2013