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Closure concept for 2-factors in claw-free graphs |
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| Authors: | Zdeněk Ryjáček Liming Xiong Kiyoshi Yoshimoto |
| Affiliation: | 1. Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic;2. Institute of Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic;3. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, PR China;4. Department of Mathematics, Jiangxi Normal University, Nanchang 330022, PR China;5. Department of Mathematics, College of Science and Technology, Nihon University, Tokyo 101-8308, Japan |
| Abstract: | We introduce a closure concept for 2-factors in claw-free graphs that generalizes the closure introduced by the first author. The 2-factor closure of a graph is uniquely determined and the closure operation turns a claw-free graph into the line graph of a graph containing no cycles of length at most 5 and no cycles of length 6 satisfying a certain condition. A graph has a 2-factor if and only if its closure has a 2-factor; however, the closure operation preserves neither the minimum number of components of a 2-factor nor the hamiltonicity or nonhamiltonicity of a graph. |
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