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arXiv · 1407.0043

Edge-colorings of $K_{m,n}$ which Forbid Multicolored Cycles

Hung-Lin Fu·Yuan-Hsun Lo·Ryo-Yu Pei
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Abstract

A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we study the proper edge-colorings of the complete bipartite graph $K_{m,n}$ which forbid multicolored cycles. Mainly, we prove that (1) for any integer $k\geq 2$, if $n\geq 5k-6$, then any properly $n$-edge-colored $K_{k,n}$ contains a multicolored $C_{2k}$, and (2) determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored $C_6$.

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Hung-Lin Fu, Yuan-Hsun Lo, Ryo-Yu Pei. 2014-06-30. Edge-colorings of $K_{m,n}$ which Forbid Multicolored Cycles. https://arxiv.org/abs/1407.0043

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