Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776958 | Discrete Mathematics | 2017 | 10 Pages |
Abstract
A 1-factor of a hypergraph G=(X,W) is a set of hyperedges such that every vertex of G is incident to exactly one hyperedge from the set. A 1-factorization is a partition of all hyperedges of G into disjoint 1-factors. The adjacency matrix of a d-uniform hypergraph G is the d-dimensional (0,1)-matrix of order |X| such that an element aα1,â¦,αd of A equals 1 if and only if α1,â¦,αd is a hyperedge of G. Here we estimate the number of 1-factors of uniform hypergraphs and the number of 1-factorizations of complete uniform hypergraphs by means of permanents of their adjacency matrices.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
A.A. Taranenko,