Bipartite graphs containing every possible pair of cycles (Q1817575)
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scientific article; zbMATH DE number 1382643
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bipartite graphs containing every possible pair of cycles |
scientific article; zbMATH DE number 1382643 |
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Bipartite graphs containing every possible pair of cycles (English)
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8 May 2000
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A result of \textit{D. Amar} [Discrete Math. 53, 1-10 (1986; Zbl 0587.05044)] states that a bipartite graph \(G = V_1 \cup V_2\) where \(|V_1|= |V_2|= n \geq 4\) for which \(d(x) + d(y) \geq n+2\) for all \(x \in V_1\) and \(y \in V_2\) contains two vertex-disjoint cycles of lengths \(2s\) and \(2t\), respectively, whenever \(s+t = n\) (\(s, t \geq 2\)). Wang extends the result to any pair \(s,t\) satisfying \(s+t \leq n\) by using a theorem of \textit{J. A. Bondy} and \textit{V. Chvátal} [Discrete Math. 15, 111-135 (1976; Zbl 0331.05138)].
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bipartite graph
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vertex-disjoint cycles
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