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Short rainbow cycles in graphs and matroids

par DeVos, Matt;Drescher, Matthew ;Funk, Daryl;González Hermosillo de la Maza, Sebastián;Guo, Krystal ;Huynh, Tony ;Mohar, Bojan;Montejano, Amanda
Référence Journal of graph theory
Publication Publié, 2020

Article révisé par les pairs

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Résumé :

Let (Formula presented.) be a simple (Formula presented.) -vertex graph and (Formula presented.) be a coloring of (Formula presented.) with (Formula presented.) colors, where each color class has size at least 2. We prove that (Formula presented.) contains a rainbow cycle of length at most (Formula presented.), which is best possible. Our result settles a special case of a strengthening of the Caccetta-Häggkvist conjecture, due to Aharoni. We also show that the matroid generalization of our main result also holds for cographic matroids, but fails for binary matroids.