A degree condition of 2-factors in bipartite graphs. (English) Zbl 0990.05105
Summary: Let \(G= (V_1,V_2; E)\) be a bipartite graph with \(|V_1|=|V_2|= n\), and \(\sigma_2(G)= \min\{d(u)+ d(v)\mid u,v\in V(G)\), \(uv\not\in E(G)\}\). We show that \(G\) has a 2-factor which exactly contains \(k\) independent cycles if \(\sigma_2(G)\geq n+2\) for any \(1\leq k\leq \lfloor (n-1)/2\rfloor\), and we also show that the result is sharp.
MSC:
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C38 | Paths and cycles |
References:
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