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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Maximum cuts in 3-uniform hypergraphs with sparse neighbourhoods
稀疏邻域 均匀超图 最大切口
2023/4/27
A cut of a hypergraph is a partition of its vertex set into two parts, and the size of the cut is the number of edges which have nonempty intersection with each of the two parts. A classical result of...
Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
Large matchings uniform hypergraphs conjectures of Erdos and Samuels Combinatorics Probability
2011/8/26
Abstract: In this paper we study conditions which guarantee the existence of perfect matchings and perfect fractional matchings in uniform hypergraphs. We reduce this problem to an old conjecture by E...
We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph.
Betti numbers of edge ideals of uniform hypergraphs
Betti number hypergraph Hilbert function Stanley-Reisner ring
2010/11/29
We describe the Betti numbers of the edge ideals I(G) of uniform hypergraphs G such that I(G) has linear graded free resolution.