A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs
| dc.creator | Caracciolo, Sergio | |
| dc.creator | Masbaum, Gregor | |
| dc.creator | Sokal, Alan D. | |
| dc.creator | Sportiello, Andrea | |
| dc.date | 2008-12-18 | |
| dc.date.accessioned | 2026-07-07T12:20:21Z | |
| dc.date.available | 2026-07-07T12:20:21Z | |
| dc.description | Consider the problem of determining whether there exists a spanning hypertree in a given k-uniform hypergraph. This problem is trivially in P for k=2, and is NP-complete for k>= 4, whereas for k=3, there exists a polynomial-time algorithm based on Lovasz' theory of polymatroid matching. Here we give a completely different, randomized polynomial-time algorithm in the case k=3. The main ingredients are a Pfaffian formula by Vaintrob and one of the authors (G.M.) for a polynomial that enumerates spanning hypertrees with some signs, and a lemma on the number of roots of polynomials over a finite field. | |
| dc.description | 6 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0812.3593 | |
| dc.identifier | http://arxiv.org/abs/0812.3593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213042 | |
| dc.subject | Computational Complexity | |
| dc.subject | Combinatorics | |
| dc.title | A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs | |
| dc.type | text |