Ore-type conditions for bipartite graphs containing hexagons |
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Authors: | Qingsong Zou Guojun Li Aijun Dong |
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Affiliation: | aSchool of Mathematics, Shandong University, Jinan, 250100, PR China |
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Abstract: | Let G=(V1,V2;E) be a bipartite graph with |V1|=|V2|=3k, where k>0. In this paper it is proved that if d(x)+d(y)≥4k−1 for every pair of nonadjacent vertices x∈V1, y∈V2, then G contains k−1 independent cycles of order 6 and a path of order 6 such that all of them are independent. Furthermore, if d(x)+d(y)≥4k for every pair of nonadjacent vertices x∈V1, y∈V2 and k>2, then G contains k−2 independent cycles of order 6 and a cycle of order 12 such that all of them are independent. |
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Keywords: | Bipartite graph Hexagon Ore-type Cycle |
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