Perfect matchings in 4-uniform hypergraphs
Copyright policy )Perfect matchings in 4-uniform hypergraphs
A perfect matching in a 4-uniform hypergraph is a subset of $\lfloor\frac{n}{4}\rfloor$ disjoint edges. We prove that if $H$ is a sufficiently large 4-uniform hypergraph on $n=4k$ vertices such that every vertex belongs to more than ${n-1\choose 3} - {3n/4 \choose 3}$ edges then $H$ contains a perfect matching. This bound is tight and settles a conjecture of H{��}n, Person and Schacht.
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), perfect matching, Vertex degrees, Hypergraphs, vertex degree, hypergraphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), perfect matching, Vertex degrees, Hypergraphs, vertex degree, hypergraphs, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Computer Science - Discrete Mathematics
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