Finding complementary cycles in locally semicomplete digraphs

Authors:
Jørgen Bang-Jensen;Morten Hegner Nielsen
Affiliations:
Department of Mathematics and Computer Science, University of Southern Denmark, DK-5230 Odense, Denmark;Department of Mathematics and Computer Science, University of Southern Denmark, DK-5230 Odense, Denmark
Venue:
Discrete Applied Mathematics
Year:
2005

Citing 3
Cited 1

Locally semicomplete digraphs: a generalization of tournaments

Journal of Graph Theory
Complementary cycles of all lengths in tournaments

Journal of Combinatorial Theory Series B
On complementary cycles in locally semicomplete digraphs

Discrete Mathematics

Minimum cycle factors in quasi-transitive digraphs

Discrete Optimization

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Abstract

It is well known that the problem of deciding whether a given digraph has a k-cycle factor for some constant k (i.e. a collection of k disjoint cycles that cover all vertices of the digraph) is NP-complete as this is a generalization of the Hamilton cycle problem. In this paper, we show that for the class of locally semicomplete digraphs the existence of a 2-cycle factor can be decided, and a 2-cycle factor found if it exists, in time O(n^3), where n is the order of the digraph.