06078945

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06078945 Faudree, J.R. Faudree, R.J. Forbidden subgraphs that imply 2-factors with a specified number of components. Bull. Inst. Comb. Appl. 64, 4-20 (2012). 2012 The Institute of Combinatorics and its Applications, Winnipeg EN Hamiltonian graph connected forbidden subgraphs Summary: The connected forbidden subgraphs and pairs of connected forbidden subgraphs that imply that any (or a sufficiently large) 2-connected graph is Hamiltonian have been characterized. Similar theorems that involve an enlarged collection of forbidden subgraph pairs that imply the existence of 2-factors have been proved, and a characterization has been given for all graphs. In this paper, a characterization of connected forbidden subgraphs and pairs of connected forbidden subgraphs that imply the existence of 2-factors with a predetermined number of components will be proved.