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Linear Ramsey numbers for bounded-degree hypergraphs

Combinatorics 2007-12-14 v2 Probability

Abstract

We show that the Ramsey number is linear for every uniform hypergraph with bounded-degree. This is a hypergraph extension of the famous theorem for ordinary graphs which Chv\'atal et al. showed in 1983. Our proof is simple, contains the multicolor case, and provides a strong embedding lemma. It shows the potential of a new hypergraph regularity lemma by the author.

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Cite

@article{arxiv.math/0612601,
  title  = {Linear Ramsey numbers for bounded-degree hypergraphs},
  author = {Yoshiyasu Ishigami},
  journal= {arXiv preprint arXiv:math/0612601},
  year   = {2007}
}

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11 pages