4 research outputs found
Finding forest-orderings of tournaments is NP-complete
Given a class of (undirected) graphs , we say that a FAS is
a -FAS if the graph induced by the edges of (forgetting their
orientations) belongs to . We show that deciding if a tournament
has a -FAS is NP-complete when is the class of all
forests. We are motivated by connections between -FAS and
structural parameters of tournaments, such as the dichromatic number, the
clique number of tournaments, and the strong Erd\H{o}s-Hajnal property
Some results and problems on tournament structure
This paper is a survey of results and problems related to the following
question: is it true that if G is a tournament with sufficiently large
chromatic number, then G has two vertex-disjoint subtournaments A,B, both with
large chromatic number, such that all edges between them are directed from A to
B? We describe what we know about this question, and report some progress on
several other related questions, on tournament colouring and domination