# Rainbow Odd Cycles

@article{Aharoni2020RainbowOC, title={Rainbow Odd Cycles}, author={Ron Aharoni and Joseph Briggs and Ron Holzman and Zilin Jiang}, journal={SIAM J. Discret. Math.}, year={2020}, volume={35}, pages={2293-2303} }

We prove that every family of (not necessarily distinct) odd cycles $O_1, \dots, O_{2\lceil n/2 \rceil-1}$ in the complete graph $K_n$ on $n$ vertices has a rainbow odd cycle (that is, a set of edges from distinct $O_i$'s, forming an odd cycle). As part of the proof, we characterize those families of $n$ odd cycles in $K_{n+1}$ that do not have any rainbow odd cycle. We also characterize those families of $n$ cycles in $K_{n+1}$, as well as those of $n$ edge-disjoint nonempty subgraphs of $K_{n…

## 6 Citations

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