A Geometric Theory for Hypergraph Matching is popular PDF and ePub book, written by Peter Keevash in 2014-12-20, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, A Geometric Theory for Hypergraph Matching can be Read Online from any device for your convenience.
A Geometric Theory for Hypergraph Matching Book PDF Summary
The authors develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: `space barriers' from convex geometry, and `divisibility barriers' from arithmetic lattice-based constructions. To formulate precise results, they introduce the setting of simplicial complexes with minimum degree sequences, which is a generalisation of the usual minimum degree condition. They determine the essentially best possible minimum degree sequence for finding an almost perfect matching. Furthermore, their main result establishes the stability property: under the same degree assumption, if there is no perfect matching then there must be a space or divisibility barrier. This allows the use of the stability method in proving exact results. Besides recovering previous results, the authors apply our theory to the solution of two open problems on hypergraph packings: the minimum degree threshold for packing tetrahedra in -graphs, and Fischer's conjecture on a multipartite form of the Hajnal-Szemerédi Theorem. Here they prove the exact result for tetrahedra and the asymptotic result for Fischer's conjecture; since the exact result for the latter is technical they defer it to a subsequent paper.
Detail Book of A Geometric Theory for Hypergraph Matching PDF
- Author : Peter Keevash
- Release : 20 December 2014
- Publisher : American Mathematical Soc.
- ISBN : 9781470409654
- Genre : Mathematics
- Total Page : 108 pages
- Language : English
- PDF File Size : 12,9 Mb
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