Abstract
We prove that a tournament with n vertices has more than 41/300 n 2(1-o(1)) arc-disjoint transitive triples, and more than 113/3000 n2 (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.
Original language | English |
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Pages (from-to) | 291-306 |
Number of pages | 16 |
Journal | Annals of Combinatorics |
Volume | 12 |
Issue number | 3 |
DOIs | |
State | Published - Oct 2008 |
Keywords
- Fractional
- Packing
- Tournament
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics