Short rainbow cycles in graphs and matroids

Abstract

AbstractLet be a simple ‐vertex graph and be a coloring of with colors, where each color class has size at least 2. We prove that contains a rainbow cycle of length at most , 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.