#### Title

Interval Tournaments

#### Document Type

Article

#### Journal/Book Title/Conference

Journal of Graph Theory

#### Volume

56

#### Issue

1

#### Publisher

Wiley Periodicals, Inc.

#### Publication Date

2007

#### First Page

72

#### Last Page

81

#### DOI

10.1002/jgt.20247

#### Abstract

A tournament is an orientation of a complete graph. A directed graph is an interval digraph if for each vertex v there corresponds an ordered pair of intervals (Sv, Tv) such that u → v if and only if Su ∩ Tv ≠ ∅. A bipartite graph is an interval bigraph if to each vertex there corresponds an interval such that vertices are adjacent if and only if their corresponding intervals intersect and each vertex belongs to a different partite set. We use the equivalence of the models for interval digraphs and interval bigraphs to characterize tournaments that are interval digraphs via forbidden subtournaments and prove that a tournament on n vertices is an interval digraph if and only if it has a transitive (n − 1)-subtournament. We also characterize the obstructions to the existence of a transitive subtournament of order n − 1 in a tournament of order n.

#### Recommended Citation

Brown, D. E., A. H. Busch and J. R. Lundgren, Interval Tournaments, Journal of Graph theory, Volume 56, no. 1, pp. 72 - 81, 2007.