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Packing 4-Cycles in Eulerian and Bipartite Eulerian Tournaments with an Application to Distances in Interchange Graphs
Raphael Yuster
Department of Mathematics, University of Haifa at Oranim, Tivon 36006, Israel
raphy@research.haifa.ac.il
Annals of Combinatorics 9 (1) p.117-124 March, 2005
AMS Subject Classification: 05C20, 05C70
Abstract:
We prove that every Eulerian orientation of Km, n contains arcdisjoint 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 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.
Keywords: tournaments, packing, cycles, interchange graphs

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