Ramsey-remainder

Paul Erdos, Zsolt Tuza, Pavel Valtr

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We investigate the following Ramsey-type problem. Given a natural number k, determine the smallest integer rr(k) such that, if n is sufficiently large with respect to k, and S is any set of n points in general position in the plane, then all but at most rr(k) points of S can be partitioned into convex sets of sizes ≥ k. We provide estimates on rr(k) which are best possible if a classic conjecture of Erdos and Szekeres on the Ramsey number for convex sets is valid. We also prove that in several types of combinatorial structures, the corresponding 'Ramsey-remainder' rr(k) is equal to the off-diagonal Ramsey number r(k, k - 1) minus 1.

Original languageEnglish
Pages (from-to)519-532
Number of pages14
JournalEuropean Journal of Combinatorics
Volume17
Issue number6
DOIs
Publication statusPublished - Aug 1996

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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