PAIRS OF FORBIDDEN CLASS OF SUBGRAPHS CONCERNING
K1,3 AND P6 TO HAVE A CYCLE CONTAINING SPECIFIED VERTICES
Department of Mathematics, Keio University
Department of Mathematical Information Science
AbstractIn , Faudree and Gould showed that if a 2-connected graph contains no K1,3 and P6 as an induced subgraph, then the graph is hamiltonian. In this paper, we consider the extension of this result to cycles passing through specified vertices. We define the families of graphs which are extension of the forbidden pair K1,3 and P6, and prove that the forbidden families implies the existence of cycles passing through specified vertices.
Keywords: forbidden subgraph, cycle.
2000 Mathematics Subject Classification: 05C38.
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Received 4 February 2008
Revised 2 January 2009
Accepted 10 March 2009