Abstract
Let H be a k-graph on n vertices, with minimum codegree at least n/k+cn for some fixed c>0. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in H or a certificate that none exists. This essentially solves a problem of Karpi\'nski, Ruci\'nski and Szyma\'nska; Szyma\'nska previously showed that this problem is NP-hard for a minimum codegree of n/k−cn. Our algorithm relies on a theoretical result of independent interest, in which we characterise any such hypergraph with no perfect matching using a family of lattice-based constructions.
Original language | English |
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Pages (from-to) | 265-334 |
Number of pages | 70 |
Journal | Advances in Mathematics |
Volume | 269 |
Early online date | 4 Nov 2014 |
DOIs | |
Publication status | Published - 10 Jan 2015 |
Keywords
- Hypergraphs
- Algorithms
- matchings