Vertex Degree Sums for Matchings in 3-Uniform Hypergraphs
نویسندگان
چکیده
منابع مشابه
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 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...
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We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose thatH is a sufficiently large 3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than ( n−1 2 )
متن کاملPerfect matching in 3 uniform hypergraphs with large vertex degree
A perfect matching in a 3-uniform hypergraph on n = 3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3-uniform hypergraph on n = 3k vertices such that every vertex belongs to at least ( n−1 2 ) − ( 2n/3 2 ) + 1 edges then H contains a perfect matching. We give a construction to show that this result is best possible.
متن کاملExact minimum degree thresholds for perfect matchings in uniform hypergraphs
Article history: Received 19 August 2011 Available online xxxx Given positive integers k and where 4 divides k and k/2 k−1, we give a minimum -degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result. Our approach makes use of the absorbing method, as well as the hypergrap...
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We study sufficient l-degree (1 ≤ l < k) conditions for the appearance of perfect and nearly perfect matchings in k-uniform hypergraphs. In particular, we obtain a minimum vertex degree condition (l = 1) for 3-uniform hypergraphs, which is approximately tight, by showing that every 3-uniform hypergraph on n vertices with minimum vertex degree at least (5/9+o(1)) ` n 2 ́ contains a perfect matchi...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8627