Geodesic
On lengths of rainbow cycles
The electronic journal of combinatorics, Tome 13 (2006)
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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 Vojtěchovský 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 a similar result does not hold for even $n$. Finally, we state several open problems in the area.
DOI : 10.37236/1131
Classification : 05C15, 05C38 
@article{10_37236_1131,
     author = {Boris Alexeev},
     title = {On lengths of rainbow cycles},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1131},
     zbl = {1111.05032},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1131/}
}
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%J The electronic journal of combinatorics
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Boris Alexeev. On lengths of rainbow cycles. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1131

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