A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs

Details A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs A randomized polynomial-time algorithm for the Spanning Hypertree Problem on 3-uniform hypergraphs

2008-12-18

arxiv.org/abs/0812.3593v1

Computer Science

Computational Complexity

6 pages, 1 figure

Scientific paper

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.

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