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girth and bi–degree, J Combin Theory Ser B 64 (1995), 228–239. MR1339850 (96i:05143)
"... Constructions of sparse uniform hypergraphs with high chromatic number. (English summary) ..."
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Constructions of sparse uniform hypergraphs with high chromatic number. (English summary)
Constructions of . . . High Chromatic Number
, 2009
"... A random construction gives new examples of simple hypergraphs with high chromatic number that have few edges and/or low maximum degree. In particular, for every integers k ≥ 2, r ≥ 2, and g ≥ 3, there exist runiform nonkcolorable hypergraphs of girth at least g with maximum degree at most ⌈rk r− ..."
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A random construction gives new examples of simple hypergraphs with high chromatic number that have few edges and/or low maximum degree. In particular, for every integers k ≥ 2, r ≥ 2, and g ≥ 3, there exist runiform nonkcolorable hypergraphs of girth at least g with maximum degree at most ⌈rk r
D.: Embeddings and Ramsey numbers of sparse kuniform hypergraphs, Combinatorica 29
, 2009
"... Abstract. Chvátal, Rödl, Szemerédi and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [5, 19] the same result was proved for 3uniform hypergraphs. Here we extend this result to kuniform hypergraphs for any integer k ≥ 3. As in the 3uni ..."
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Cited by 19 (4 self)
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Abstract. Chvátal, Rödl, Szemerédi and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [5, 19] the same result was proved for 3uniform hypergraphs. Here we extend this result to kuniform hypergraphs for any integer k ≥ 3. As in the 3
Hypergraphs with Zero Chromatic Threshold
, 1307
"... Let F be an runiform hypergraph. The chromatic threshold of the family of Ffree, runiform hypergraphs is the infimum of all nonnegative reals c such that the subfamily of Ffree, runiform hypergraphs H with minimum degree at least c (V(H)) r−1 has bounded chromatic number. The study of chroma ..."
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Let F be an runiform hypergraph. The chromatic threshold of the family of Ffree, runiform hypergraphs is the infimum of all nonnegative reals c such that the subfamily of Ffree, runiform hypergraphs H with minimum degree at least c (V(H)) r−1 has bounded chromatic number. The study
The Chromatic Numbers of Random Hypergraphs
 Random Struct. Alg
, 1998
"... : For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number of t ..."
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Cited by 2 (1 self)
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: For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number
On the chromatic number of Kneser hypergraphs
, 2000
"... We give a simple and elementary proof of Kr'iz's lower bound on the chromatic number of the Kneser rhypergraph of a set system S. ..."
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Cited by 5 (1 self)
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We give a simple and elementary proof of Kr'iz's lower bound on the chromatic number of the Kneser rhypergraph of a set system S.
Ramsey numbers of sparse hypergraphs
"... We give a short proof that any kuniform hypergraph H on n vertices with bounded degree ∆ has Ramsey number at most c(∆, k)n, for an appropriate constant c(∆, k). This result was recently proved by several authors, but those proofs are all based on applications of the hypergraph regularity method. H ..."
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Cited by 3 (1 self)
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We give a short proof that any kuniform hypergraph H on n vertices with bounded degree ∆ has Ramsey number at most c(∆, k)n, for an appropriate constant c(∆, k). This result was recently proved by several authors, but those proofs are all based on applications of the hypergraph regularity method
On the chromatic number of a random hypergraph
, 2012
"... We consider the problem of kcolouring a random runiform hypergraph with n vertices and cn edges, where k, r, c remain constant as n → ∞. Achlioptas and Naor showed that the chromatic number of a random graph in this setting, the case r = 2, must have one of two easily computable values as n → ∞. W ..."
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Cited by 2 (0 self)
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We consider the problem of kcolouring a random runiform hypergraph with n vertices and cn edges, where k, r, c remain constant as n → ∞. Achlioptas and Naor showed that the chromatic number of a random graph in this setting, the case r = 2, must have one of two easily computable values as n
Results 1  10
of
128,964