2 research outputs found
Vertex degree sums for perfect matchings in 3-uniform hypergraphs
We determine the minimum degree sum of two adjacent vertices that ensures a
perfect matching in a 3-graph without isolated vertex. More precisely, suppose
that is a 3-uniform hypergraph whose order is sufficiently large and
divisible by . If contains no isolated vertex and for any two vertices and that are
contained in some edge of , then contains a perfect matching. This bound
is tight
Vertex degree sums for matchings in 3-uniform hypergraphs
Let be positive integers such that is sufficiently large and . Suppose is a 3-uniform hypergraph of order . If contains no
isolated vertex and for any two vertices and
that are contained in some edge of , then contains a matching of
size . This degree sum condition is best possible and confirms a conjecture
of the authors [Electron. J. Combin. 25 (3), 2018], who proved the case when
.Comment: arXiv admin note: text overlap with arXiv:1710.0475