Hamiltonian Connected Line Graphs

Authors:
Deng-Xin Li;Hong-Jian Lai;Ye-Hong Shao;Mingquan Zhan
Affiliations:
College of sicence, Chongqing Technology and, Business University, Chongqing, 400067, P.R. China;Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, ;Arts and Science, Ohio University, Southern, Ironton, OH 45638, ;Department of Mathematics, Millersville University, Millersville, PA 17551,
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
Year:
2007

Citing 3
Cited 0

On a closure concept in claw-free graphs

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications
On factors of 4-connected claw-free graphs

Journal of Graph Theory

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Abstract

Thomassen conjectured [8] that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K 5 驴 E(C), where C is a cycle of length 4 in K 5. In [2], it is shown that every 4-connected line graph without an induced subgraph isomorphic to the hourglass is hamiltonian connected. In this note, we prove that every 3-connected, essentially 4-connected hourglass-free line graph is hamiltonian connected.