# An approximate version of Jackson's conjecture

• Yani Pehova (University of Warwick)
• Thursday 21 November 2019, 14:30-15:30
• MR12.

In 1981 Jackson showed that the diregular bipartite tournament (a complete bipartite graph whose edges are oriented so that every vertex has the same in- and outdegree) contains a Hamilton cycle, and conjectured that in fact the edge set of it can be partitioned into Hamilton cycles. We prove an approximate version of this conjecture: For every $c > 1/2$ and $\varepsilon > 0$ there exists $n_0$ such that every $cn$-regular bipartite digraph on $2n\geq n_0$ vertices contains $(1 – \varepsilon)cn$ edge-disjoint Hamilton cycles.

This talk is part of the Combinatorics Seminar series.