Packing 4-cycles in Eulerian and bipartite Eulerian tournaments with an application to distances in interchange graphs
نویسنده
چکیده
We prove that every Eulerian orientation of Km,n contains 1 4+ √ 8 mn(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 1 8+ √ 32 n2(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. Ams classification code: 05C20; 05C70
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