3-Uniform hypergraphs of bounded degree have linear Ramsey numbers

Details 3-Uniform hypergraphs of bounded degree have linear Ramsey numbers 3-Uniform hypergraphs of bounded degree have linear Ramsey numbers

2006-08-17

arxiv.org/abs/math/0608442v1

Mathematics

Combinatorics

19 pages, 1 figure, submitted to J. Comb. Theory Ser. B

Scientific paper

Chv\'atal, R\"odl, Szemer\'edi and Trotter proved that the Ramsey numbers of
graphs of bounded maximum degree are linear in their order. We prove that the
same holds for 3-uniform hypergraphs. The main new tool which we prove and use
is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into
suitable 3-uniform `pseudo-random' hypergraphs.

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