## Asymptotic Bounds for Classical Ramsey Numbers |

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### Contents

Introduction | |

Ramseys Theorem 18 | |

Known Ramsey Numbers 36 | |

Copyright | |

5 other sections not shown

### Common terms and phrases

2-coloring asymptotic bounds blue monochromatic called classical Ramsey numbers classical Ramsey theory combinatorial complete graph complete subgraph consider contains convex hull convex polygon corollary to Theorem countable countable set cubic residues DEFINITION denote edges of G endpoint Entscheidungsproblem Erdos and Spencer Erdos and Szekeres Erdos's lower bound finite follows Graham and Rothschild graph G Graver and Yackel Greenwood and Gleason hypergraphs inequalities infinite integers Legendre symbol logy monochromatic blue monochromatic subgraph nonempty nontrivial Ramsey number number of red number of vertices NX(E obtain pigeonhole principle points positive integers probabilistic method problem proof of Theorem proper transversal Property prove quadratic nonresidue quadratic residues Ramsey's theorem real numbers red and blue represent the number result satisfies Lemma set of vertices specific Ramsey numbers specify subsets sufficiently large Theorem 6.2 third proof total number uncountable upper bound vertex coloring vertex set yields