Short Rainbow Cycles in Sparse Graphs

Wed, Mar 7, 2018 11:00 CET

Speakers: Tony Huynh

Tags: Graphs, Rainbow Cycles

Let \(G\) be a simple \(n\)-vertex graph and \(c\) be a colouring of \(E(G)\) with \(n\) colours, where each colour class has size at least \(2\). We prove that \(G\) contains a rainbow cycle of length at most \(\lceil \frac{n}{2} \rceil\), 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.

This is joint work with Matt DeVos, Krystal Guo, Daryl Funk, Bojan Mohar, and Amanda Montejano.