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Keywords:

  • toughness;
  • forbidden subgraph

Abstract

Let inline image be a family of connected graphs. A graph G is said to be inline image-free if G is H-free for every graph H in inline image. 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 inline image such that every large enough connected inline image-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