Claws contained in all n-tournaments

Largest digraphs contained in all n-tournaments

A directed graph G is an unavoidable subgraph o f all n-tournaments or, simply n-unavoidable, if every tournament on n vertices contain san isomorphic copy o f G, i.e., for each ntournament T there exists an edge preserving injection o f the vertices o f G into the vertices o f T. The problem o f showing certain types o f graphs to be n-unavoidable has been the subject o f several papers, for e...

When n-cycles in n-partite tournaments are longest cycles

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

The Winner-Take-All Principle in Small Tournaments

An Optimal Algorithm for Finding All Convex Subsets in Tournaments

A tournament is a complete directed graph. A convex subset is a vertex subset with the property that every two-path beginning and ending inside the convex subset is contained completely within the subset. This paper shows a relationship between convex subsets and transitive closures which leads to an optimal O(n 3)-time algorithm for nding all convex subsets in a tournament.

Bounds and constructions for n-e.c. tournaments

Few families of tournaments satisfying the n-e.c. adjacency property are known. We supply a new random construction for generating infinite families of vertex-transitive n-e.c. tournaments by considering circulant tournaments. Switching is used to generate new ne.c. tournaments of certain orders. With aid of a computer search, we demonstrate that there is a unique minimum order 3-e.c. tournamen...