Long paths with endpoints in given vertex-subsets of graphs |
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Authors: | Hao Li Jianping Li |
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Institution: | a LRI, Université de Paris-Sud and CNRS, Orsay F-91405, France b Department of Mathematics, Yunnan University, Kunming 650091,China c School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China |
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Abstract: | Let G=(V,E) be a connected graph of order n, t a real number with t?1 and M⊆V(G) with . In this paper, we study the problem of some long paths to maintain their one or two different endpoints in M. We obtain the following two results: (1) for any vertex v∈V(G), there exists a vertex u∈M and a path P with the two endpoints v and u to satisfy , , dG(u)+1-t}; (2) there exists either a cycle C to cover all vertices of M or a path P with two different endpoints u0 and up in M to satisfy , where . |
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Keywords: | 05c38 05c45 05c35 |
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