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Discussiones Mathematicae Graph Theory 24(1) (2004) 47-54
DOI: https://doi.org/10.7151/dmgt.1212
FORBIDDEN TRIPLES IMPLYING HAMILTONICITY: FOR ALL GRAPHS
Ralph J. Faudree
University of Memphis Memphis, TN 38152, USA |
Ronald J. Gould
Emory University Atlanta, GA 30322, USA |
Michael S. Jacobson
University of Colorado at Denver Denver, CO 80217, USA |
Abstract
In [2], Brousek characterizes all triples of graphs, G1,G2, G3, with Gi = K1,3 for some i = 1, 2, or 3, such that all G1 G2 G3-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G1, G2, G3, none of which is a K1,s, s ≥ 3 such that G1, G2, G3-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G1, G2, G3 with none being K1,3, such that all G1 G2G3-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G1, G2, G3 such that all G1 G2 G3-free graphs are hamiltonian.Keywords: hamiltonian, induced subgraph, forbidden subgraphs.
2000 Mathematics Subject Classification: primary: 05C, secondary: 05C35, 05C45.
References
[1] | P. Bedrossian, Forbidden Subgraph and Minimum Degree Conditions for Hamiltonicity (Ph.D. Thesis, Memphis State University, 1991). |
[2] | J. Brousek, Forbidden Triples and Hamiltonicity, Discrete Math. 251 (2002) 71-76, doi: 10.1016/S0012-365X(01)00326-0. |
[3] | G. Chartrand and L. Lesniak, Graphs & Digraphs (3rd Edition, Chapman & Hall, 1996). |
[4] | R.J. Faudree and R.J. Gould, Characterizing Forbidden Pairs for Hamiltonian Properties, Discrete Math. 173 (1997) 45-60, doi: 10.1016/S0012-365X(96)00147-1. |
[5] | R.J. Faudree, R.J. Gould and M.S. Jacobson, Potential Forbidden Triples Implying Hamiltonicity: For Sufficiently Large Graphs, preprint. |
[6] | R.J. Faudree, R.J. Gould, M.S. Jacobson and L. Lesniak, Characterizing Forbidden Clawless Triples for Hamiltonian Graphs, Discrete Math. 249 (2002) 71-81, doi: 10.1016/S0012-365X(01)00235-7. |
Received 15 March 2001
Revised 25 April 2003