Semicomplete absorbent sets in digraphs

QCSP on Semicomplete Digraphs

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over semicomplete digraphs. We obtain a complexity-theoretic trichotomy: QCSP(H) is either in P, is NP-hard or is Pspace-complete. The largest part of our work is the algebraic classification of precisely which semicompletes enjoy only essentially unary polymorphisms, which is combinatorially interesting i...

Kings in semicomplete multipartite digraphs

A digraph obtained by replacing each edge of a complete p-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicom-plete p-partite digraph, or just a semicomplete multipartite digraph. A semicomplete multipartite digraph with no cycle of length two is a multipartite tournament. In a digraph D, an r-king is a vertex q such that every vertex in D ...

Cycles in Semicomplete Multipartite Digraphs

Spanning Local Tournaments in Locally Semicomplete Digraphs

We investigate the existence of a spanning local tournament with possibly high connectivity in a highly connected locally semicomplete digraph. It is shown that every (3k 2)-connected locally semicomplete digraph contains a k-connected spanning local tournament. This improves the result of Bang-Jensen and Thomassen for semicomplete digraphs and of Bang-Jensen [I] for locally semicomplete digrap...

One-diregular subgraphs in semicomplete multipartite digraphs

The problem of nding necessary and suucient conditions for a semicomplete multipartite digraphs (SMD) to be Hamiltonian, seems to be both very interesting and diicult. In 3] Bang-Jensen, Gutin and Huang proved a suucient condition for a SMD to be Hamiltonian. A strengthening of this condition, shown in this paper, allows us to prove the following three results. We prove that every k-strong SMD ...