Seminar Details

Suppose G is a d-regular digraph. How large does d need to be to guarantee the existence of a directed cycle with length divisible by k? We prove that d >= 25k suffices. The previous best bound was roughly d >= k log k by Alon and Linial using the local lemma. Our proof generalizes a determinant-permanent framework introduced by Friedland. We will discuss the proof of the main result and mention some extensions to zero sum cycle packing.