Restricted cycle factors and arc-decompositions of digraphs

Funding Agencies|Danish Research Council [1323-00178B]; Institute Mittag-Leffler
We study the complexity of finding 2-factors with various restrictions as well as edge-decompositions in (the underlying graphs of) digraphs. In particular we show that it is N P-complete to decide whether the underlying undirected graph of a digraph D has a 2-factor with cycles C-1, C-2, ..., C-k such that at least one of the cycles C-i is a directed cycle in D (while the others may violate the orientation back in D). This solves an open problem from J. Bang-Jensen et al., Vertex-disjoint directed and undirected cycles in general digraphs, JCT B 106 (2014), 1-14. Our other main result is that it is also N P-complete to decide whether a 2-edge-colored bipartite graph has two edge-disjoint perfect matchings such that one of these is monochromatic (while the other does not have to be). We also study the complexity of a number of related problems. In particular we prove that for every even k greater than= 2, the problem of deciding whether a bipartite digraph of girth k has a k-cycle-free cycle factor is N P-complete. Some of our reductions are based on connections to Latin squares and so-called avoidable arrays.

NATURVETENSKAP Matematik hsv//swe
NATURAL SCIENCES Mathematics hsv//eng
Cycle factor; 2-factor; Mixed problem; NP-complete; Complexity; Cycle factors with no short cycles; Latin square; Avoidable arrays; Monochromatic matchings

Casselgren, Carl JohanLinköpings universitet,Matematik och tillämpad matematik,Tekniska fakulteten(Swepub:liu)carca15 (författare)
University of Southern Denmark, DenmarkMatematik och tillämpad matematik (creator_code:org_t)

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