• Corpus ID: 228063944

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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