Bi-cycle extendable through a given set in balanced bipartite graphs |
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Authors: | Hao Li |
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Institution: | a Department of Mathematics, West Virginia University, Morgantown, WV 26505, USA b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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Abstract: | Let G=(X,Y;E) be a balanced bipartite graph of order 2n. The path-cover numberpc(H) of a graph H is the minimum number of vertex-disjoint paths that use up all the vertices of H. S⊆V(G) is called a balanced set of G if |S∩X|=|S∩Y|. In this paper, we will give some sufficient conditions for a balanced bipartite graph G satisfying that for every balanced set S, there is a bi-cycle of every length from |S|+2pc(〈S〉) up to 2n through S. |
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Keywords: | Balanced bipartite graph Bi-cycle extendable Balanced set |
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