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.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics