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Tiling 3‐Uniform Hypergraphs With K 4 3 − 2 e
Author(s) -
Czygrinow Andrzej,
DeBiasio Louis,
Nagle Brendan
Publication year - 2014
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21726
Subject(s) - mathematics , combinatorics , hypergraph , disjoint sets , integer (computer science) , vertex (graph theory) , order (exchange) , discrete mathematics , graph , finance , computer science , economics , programming language
LetK 4 3 − 2 e denote the hypergraph consisting of two triples on four points. For an integer n , let t ( n , K 4 3 − 2 e ) denote the smallest integer d so that every 3‐uniform hypergraph G of order n with minimum pair‐degreeδ 2 ( G ) ≥ d contains ⌊ n / 4 ⌋ vertex‐disjoint copies ofK 4 3 − 2 e . Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767–821) proved that t ( n , K 4 3 − 2 e ) = n 4 ( 1 + o ( 1 ) )holds for large integers n . Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4,A main ingredient in our proof is the recent “absorption technique” of Rödl, Ruciński, and Szemerédi (J. Combin. Theory Ser. A 116(3) (2009), 613–636).