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#### Speaker - Tony Huynh

Short Rainbow Cycles in Sparse Graphs Wed, Mar 7, 2018 11:00 CET

###### Speakers:Tony Huynh

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.

Transfinite Ford-Fulkerson on a Finite Network Wed, Nov 23, 2016 12:00 CET

###### Speakers:Tony Huynh

Today Tony will tell us about Transfinite Ford-Fulkerson on a Finite Network.