Abstract
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 Chvatal et al. [V. Chvatal, V. Rodl, E. Szemeredi and W.T. Trotter, Jr., The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory Ser. B 34 (1983), pp. 239–243] showed in 1983. Our proof demonstrates the potential of a new regularity lemma by [Y. Ishigami, A simple regularization of hypergraphs, preprint, arXiv:math/0612838 (2006)].
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