论文信息 - Traceability in Small Claw-Free Graphs

Traceability in Small Claw-Free Graphs

Abstract We prove that a claw-free, 2-connected graph with fewer than 18 vertices is traceable, and we determine all non-traceable, claw-free, 2-connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs.

John M. Harris | Michael J. Mossinghoff

[1] L. Markus. Hamiltonian Results in K(l,r)-Free Graphs , 1993 .

[2] David P. Sumner,et al. Hamiltonian results in K1, 3-free graphs , 1984, J. Graph Theory.

[3] Zdenek Ryjácek,et al. Claw-free graphs - A survey , 1997, Discret. Math..

[4] Zdenek Ryjácek. On a Closure Concept in Claw-Free Graphs , 1997, J. Comb. Theory, Ser. B.

[5] H. Whitney. Congruent Graphs and the Connectivity of Graphs , 1932 .

[6] Zdeněk Ryjáčk. On a Closure Concept in Claw-Free Graphs , 1997 .

[7] Chie Nara. On Sufficient Conditions for a Graph to be Hamiltonian , 1980 .

[8] Zdzislaw Skupien,et al. On traceability and 2-factors in claw-free graphs , 2004, Discuss. Math. Graph Theory.