A multi-dimensional Szemerédi theorem for the primes via a correspondence principle
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چکیده
منابع مشابه
A multipartite Hajnal-Szemerédi theorem
The celebrated Hajnal-Szemerédi theorem gives the precise minimum degree threshold that forces a graph to contain a perfect Kk-packing. Fischer’s conjecture states that the analogous result holds for all multipartite graphs except for those formed by a single construction. Recently, we deduced an approximate version of this conjecture from new results on perfect matchings in hypergraphs. In thi...
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We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. The seminal Hajnal–Szemerédi theorem [12] characterises the minimum degree that ensures a graph G contains a perfect Kr-packing. Balogh, Kostochka and Treglown [4] proposed a degree sequence version of the Hajnal–Szemerédi theorem which, if true, gives a strength...
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For a positive integer r ≥ 2, a Kr-factor of a graph is a collection vertex-disjoint copies of Kr which covers all the vertices of the given graph. The celebrated theorem of Hajnal and Szemerédi asserts that every graph on n vertices with minimum degree at least (1− 1r )n contains a Kr-factor. In this note, we propose investigating the relation between minimum degree and existence of perfect Kr...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2015
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-015-1157-9