The Complexity of Almost Perfect Matchings in Uniform Hypergraphs with High Codegree

Authors:
Edyta Szymańska
Affiliations:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Venue:
Combinatorial Algorithms
Year:
2009

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Abstract

In this paper we prove that the problem APM(k,r,c) of deciding whether a given k 驴uniform hypergraph H, with minimum (k 驴 1) 驴wise vertex degree at least c|V(H)|, contains a matching missing exactly r vertices, that is, a set of disjoint edges of size at least (|V(H)| 驴 r)/k, is NP-complete for $c while for $c\frac 1k,$ and r 0 we provide a polynomial time algorithm for the corresponding search problem.