Packing 4-Cycles in Eulerian and Bipartite Eulerian Tournaments with an Application to Distances in Interchange Graphs期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Packing 4-Cycles in Eulerian and Bipartite Eulerian Tournaments with an Application to Distances in Interchange Graphs

Authors:	Raphael Yuster

Institution:	(1) Department of Mathematics, University of Haifa at Oranim, Tivon, 36006, Israel

Abstract:	We prove that every Eulerian orientation of K_m,n contains $\tfrac{1} {{4 + \sqrt 8 }}mn(1 - o(1))$ 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 $\tfrac{1} {{8 + \sqrt {32} }}n^2 (1 - o(1))$ 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.Received February 6, 2004

Keywords:	05C20 05C70
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