Bi-cycle extendable through a given set in balanced bipartite graphs

Authors:
Hao Li;Mei Lu
Affiliations:
Department of Mathematics, West Virginia University, Morgantown, WV 26505, USA;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Venue:
Discrete Applied Mathematics
Year:
2009

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Extending cycles in bipartite graphs

Journal of Combinatorial Theory Series B
Minimum Degree Conditions for Cycles Including Specified Sets of Vertices

Graphs and Combinatorics
Graph Theory With Applications

Graph Theory With Applications

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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() up to 2n through S.