Non-separating 2-factors of an even-regular graph |
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| Authors: | Yusuke Higuchi Yuji Nomura |
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| Affiliation: | a Mathematics Laboratories, College of Arts and Sciences, Showa University, 4562 Kamiyoshida, Fujiyoshida, Yamanashi 403-0005, Japan
b Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan |
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| Abstract: | For a 2-factor F of a connected graph G, we consider G−F, which is the graph obtained from G by removing all the edges of F. If G−F is connected, F is said to be a non-separating 2-factor. In this paper we study a sufficient condition for a 2r-regular connected graph G to have such a 2-factor. As a result, we show that a 2r-regular connected graph G has a non-separating 2-factor whenever the number of vertices of G does not exceed 2r2+r. |
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| Keywords: | 2-factor Non-separating Even-regular graph |
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