Edge-colorings of \(K_{m,n}\) which forbid multicolored cycles (Q2848790)
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scientific article; zbMATH DE number 6212226
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Edge-colorings of \(K_{m,n}\) which forbid multicolored cycles |
scientific article; zbMATH DE number 6212226 |
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26 September 2013
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edge coloring
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multicolored cycle
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complete bipartite graph
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math.CO
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Edge-colorings of \(K_{m,n}\) which forbid multicolored cycles (English)
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A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, the authors study the proper edge colorings of the complete bipartite graph \(K_{m, n}\) which forbid multicolored cycles. It is proved that for any integer \(k \geq 2\), if \(n \geq 5k - 6\), then any properly \(n\)-edge colored \(K_{k, n}\) contains a multicolored \(C_{2k}\). The authors also determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored \(C_6\).
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