# Rainbow and monochromatic circuits and cuts in binary matroids

@article{Berczi2020RainbowAM, title={Rainbow and monochromatic circuits and cuts in binary matroids}, author={Krist'of B'erczi and Tam{\'a}s Schwarcz}, journal={ArXiv}, year={2020}, volume={abs/2012.05037} }

Given a matroid together with a coloring of its ground set, a subset of its elements is called rainbow colored if no two of its elements have the same color. We show that if a binary matroid of rank $r$ is colored with exactly $r$ colors, then $M$ either contains a rainbow colored circuit or a monochromatic cut. As the class of binary matroids is closed under taking duals, this immediately implies that $M$ either contains a rainbow colored cut or a monochromatic circuit as well. As a byproduct…

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Rainbow Odd Cycles

- MathematicsSIAM J. Discret. Math.
- 2021

It is proved that every family of (not necessarily distinct) odd cycles 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).

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