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Hamiltonian connected hourglass free line graphs |
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| Authors: | Li Dengxin Yehong Shao |
| Institution: | a Department of Mathematics, Chongqing Technology and Businness University, Chongqing 400020, PR China b Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA c Arts and Science, Ohio University Southern, Ironton, OH 45638, USA d Department of Mathematics, Millersville University, Millersville, PA 17551, USA |
| Abstract: | Thomassen Reflections on graph theory, J. Graph Theory 10 (1986) 309-324] conjectured that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K5-E(C4), where C4 is a cycle of length 4 in K5. In Broersma et al. On factors of 4-connected claw-free graphs, J. Graph Theory 37 (2001) 125-136], 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. |
| Keywords: | Hamiltonian connected graph Line graph Hourglass free graph |
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