113 research outputs found
A Stability Theorem for Matchings in Tripartite 3-Graphs
It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most (1 + ϵ)n/2 is close in structure to the extremal configuration, where ‘closeness’ is measured by an explicit function of ϵ.Natural Sciences and Engineering Research Counci
A Stability Theorem for Matchings in Tripartite 3-Graphs
It follows from known results that every regular tripartite hypergraph of positive degree, with n vertices in each class, has matching number at least n/2. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most (1 + ϵ)n/2 is close in structure to the extremal configuration, where ‘closeness’ is measured by an explicit function of ϵ.Natural Sciences and Engineering Research Counci
Random multi-index matching problems
The multi-index matching problem (MIMP) generalizes the well known matching
problem by going from pairs to d-uplets. We use the cavity method from
statistical physics to analyze its properties when the costs of the d-uplets
are random. At low temperatures we find for d>2 a frozen glassy phase with
vanishing entropy. We also investigate some properties of small samples by
enumerating the lowest cost matchings to compare with our theoretical
predictions.Comment: 22 pages, 16 figure
Monochromatic connected matchings in 2-edge-colored multipartite graphs
A matching in a graph is connected if all the edges of are in the
same component of . Following \L uczak,there have been many results using
the existence of large connected matchings in cluster graphs with respect to
regular partitions of large graphs to show the existence of long paths and
other structures in these graphs. We prove exact
Ramsey-type bounds on the sizes of monochromatic connected matchings in
-edge-colored multipartite graphs. In addition, we prove a stability theorem
for such matchings.Comment: 29 pages, 2 figure
Hypergraph matchings and designs
We survey some aspects of the perfect matching problem in hypergraphs, with
particular emphasis on structural characterisation of the existence problem in
dense hypergraphs and the existence of designs.Comment: 19 pages, for the 2018 IC
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