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Packing Transitive Triples in a Tournament
Department of Mathematics, University of Haifa, Haifa 31905, Israel
mkabiya@yahoo.com, raphy@research.haifa.ac.il
Annals of Combinatorics 12 (3) pp.291-306 September, 2008
AMS Subject Classification: 05C20, 05C70
Abstract:
We prove that a tournament with $n$ vertices has more than $\frac{41}{300}n^2(1-o(1))$ arc-disjoint transitive triples, and more than $\frac{113}{3000}n^2(1-o(1))$ arc-disjoint transitive quadruples, improving earlier bounds. In particular, $82$ percent of the arcs of a tournament can be packed with transitive triples and $45$ percent of the arcs of a tournament can be packed with transitive quadruples. Our proof is obtained by examining the fractional version of the problem and utilizing a connection between the integral and fractional versions.
Keywords: tournament, packing, fractional

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