On lengths of rainbow cycles

Details On lengths of rainbow cycles On lengths of rainbow cycles

2005-07-22

arxiv.org/abs/math/0507456v4

Electron. J. Combin. 13 (2006), no. 1, Research Paper 105, 14 pp. (electronic)

Mathematics

Combinatorics

10 pages, 7 figures, 1 table. Replaced version (v2) includes a new result, some computer experimentation, and more. The next v

Scientific paper

We prove several results regarding edge-colored complete graphs and rainbow cycles, cycles with no color appearing on more than one edge. We settle a question posed by Ball, Pultr, and Vojt\v{e}chovsk\'{y} by showing that if such a coloring does not contain a rainbow cycle of length $n$, where $n$ is odd, then it also does not contain a rainbow cycle of length $m$ for all $m$ greater than $2n^2$. In addition, we present two examples which demonstrate that this result does not hold for even $n$. Finally, we state several open problems in the area.

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