Vertex Degree Sums for Perfect Matchings in 3-uniform Hypergraphs
نویسندگان
چکیده
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 H is a 3-uniform hypergraph whose order n is sufficiently large and divisible by 3. If H contains no isolated vertex and deg(u)+deg(v) > 2 3 n2− 8 3 n+2 for any two vertices u and v that are contained in some edge of H, then H contains a perfect matching. This bound is tight.
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