Packing 4-cycles in Eulerian and bipartite Eulerian tournaments with an application to distances in interchange graphs

الأصل · EN

We prove that every Eulerian orientation of Kₘ,ₙ contains 14+√8mn(1-o(1)) arc-disjoint directed 4-cycles, improving earlier lower bounds. Combined with a probabilistic argument, this result is used to prove that every regular tournament with n vertices contains 18+√32n²(1-o(1)) arc-disjoint directed 4-cycles. The result is also used to provide an upper bound for the distance between two antipodal vertices in interchange graphs.