Abstract
Let H be a given graph. A graph G is said to be H-free if G contains no induced copies of H. For a class of graphs, the graph G is -free if G is H-free for every . Bedrossian characterized all the pairs of connected subgraphs such that every 2-connected -free graph is hamiltonian. Faudree and Gould extended Bedrossian's result by proving the necessity part of the result based on infinite families of non-hamiltonian graphs. In this article, we characterize all pairs of (not necessarily connected) graphs such that there exists an integer n0 such that every 2-connected -free graph of order at least n0 is hamiltonian.
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