scholarly journals Perfect matchings in large uniform hypergraphs with large minimum collective degree

2009 ◽  
Vol 116 (3) ◽  
pp. 613-636 ◽  
Author(s):  
Vojtech Rödl ◽  
Andrzej Ruciński ◽  
Endre Szemerédi
Keyword(s):  
Perfect Matchings ◽  
Uniform Hypergraphs ◽  
Collective Degree

Nearly Perfect Matchings in Uniform Hypergraphs

2021 ◽  
Vol 35 (2) ◽  
pp. 1022-1049
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Xiaofan Yuan
Keyword(s):  
Perfect Matchings ◽  
Uniform Hypergraphs

scholarly journals Near Perfect Matchings ink-Uniform Hypergraphs

2014 ◽  
Vol 24 (5) ◽  
pp. 723-732 ◽  
Author(s):  
JIE HAN
Keyword(s):  
Perfect Matchings ◽  
Large Integer ◽  
Uniform Hypergraph ◽  
Uniform Hypergraphs

LetHbe ak-uniform hypergraph onnvertices wherenis a sufficiently large integer not divisible byk. We prove that if the minimum (k− 1)-degree ofHis at least ⌊n/k⌋, thenHcontains a matching with ⌊n/k⌋ edges. This confirms a conjecture of Rödl, Ruciński and Szemerédi [13], who proved that minimum (k− 1)-degreen/k+O(logn) suffices. More generally, we show thatHcontains a matching of sizedif its minimum codegree isd<n/k, which is also best possible.

On Perfect Matchings in Uniform Hypergraphs with Large Minimum Vertex Degree

2009 ◽  
Vol 23 (2) ◽  
pp. 732-748 ◽  
Author(s):  
Hip Hàn ◽  
Yury Person ◽  
Mathias Schacht
Keyword(s):  
Perfect Matchings ◽  
Vertex Degree ◽  
Uniform Hypergraphs

Disjoint perfect matchings in 3-uniform hypergraphs

2017 ◽  
Vol 88 (2) ◽  
pp. 284-293
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Li Zhang
Keyword(s):  
Perfect Matchings ◽  
Uniform Hypergraphs

scholarly journals Perfect Matchings in Random r-regular, s-uniform Hypergraphs

1996 ◽  
Vol 5 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Colin Cooper ◽  
Alan Frieze ◽  
Michael Molloy ◽  
Bruce Reed
Keyword(s):  
High Probability ◽  
Perfect Matching ◽  
Perfect Matchings ◽  
Expected Number ◽  
Uniform Hypergraphs ◽  
The Difference

We show that r-regular, s-uniform hypergraphs contain a perfect matching with high probability (whp), provided The Proof is based on the application of a technique of Robinson and Wormald [7, 8]. The space of hypergraphs is partitioned into subsets according to the number of small cycles in the hypergraph. The difference in the expected number of perfect matchings between these subsets explains most of the variance of the number of perfect matchings in the space of hypergraphs, and is sufficient to prove existence (whp), using the Chebychev Inequality.

Sign in / Sign up

Export Citation Format

Share Document