On 2-factors with cycles containing specified edges in a bipartite graph |
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Authors: | Jin Yan Guizhen Liu |
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Institution: | School of Mathematics and Systems Sciences, Shandong University, Jinan 250100, China |
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Abstract: | Let k≥1 be an integer and G=(V1,V2;E) a bipartite graph with |V1|=|V2|=n such that n≥2k+2. In this paper it has been proved that if for each pair of nonadjacent vertices x∈V1 and y∈V2, , then for any k independent edges e1,…,ek of G, G has a 2-factor with k+1 cycles C1,…,Ck+1 such that ei∈E(Ci) and |V(Ci)|=4 for each i∈{1,…,k}. We shall also show that the conditions in this paper are sharp. |
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Keywords: | Bipartite graph Cycle Quadrilateral 2-factor |
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