The theory of directed graphs has developed enormously over recent decades, yet this book
(first published in 2000) remains the only book to cover more than a small fraction of the …

Our main result is a linear-time (that is, time O(m+n)) algorithm to recognize and represent
proper circular-arc graphs. The best previous algorithm, due to A. Tucker, has time …

A tournament is an orientation of a complete graph, and in general a multipartite tournament
is an orientation of a complete n-partite graph. Many results about cycles in tournaments are …

A digraph is quasi‐transitive if there is a complete adjacency between the inset and the
outset of each vertex. Quasi‐transitive digraphs are interseting because of their relation to …

In this paper we introduce a generalization of digraphs that are locally tournaments (and
hence of tournaments). This is the class of in-tournament digraphs-the set of predecessors of …

Recently, Huang (1995) gave a characterization of local tournaments. His characterization
involves arc-reversals and therefore may not be easily used to solve other structural …

We survey results concerning various generalizations of tournaments. The reader will see
that tournaments are by no means the only class of directed graphs with a very rich structure …

We describe a new type of sufficient condition for a digraph to be Hamiltonian. Conditions of
this type combine local structure of the digraph with conditions on the degrees of …

Circular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are
the intersection graphs of chords on a circle. These graph classes have been the subject of …

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally
semicomplete if the out-neighbourhood and in-neighbourhood of any vertex induce a …