Hamilton cycles in 6-connected claw-free graphs (Extended abstract) |
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| Institution: | 1. School of Mathematics, Shandong University, Jinan 250100, China;2. School of Management, Qufu Normal University, Rizhao 276826, China;1. College of Liberal Arts and Science, Kitasato University, 1-15-1 Kitasato, Minami-ku, Sagamihara, Kanagawa 252-0373, Japan;2. Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa, 223-8522, Japan;1. University of Pretoria, Private Bag X20, Hatfield 0028, South Africa;2. DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa;3. University of South Africa, P.O. Box 392, UNISA, 0003, South Africa |
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| Abstract: | Thomassen conjectured in 1986 that every 4-connected line graph is hamiltonian. In this paper, we show that 6-connected line graphs are hamiltonian, improving on an analogous result for 7-connected line graphs due to Zhan in 1991. Our result implies that every 6-connected claw-free graph is hamiltonian. |
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