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Linear Ramsey Numbers

  • Aistis Atminas
  • Vadim LozinEmail author
  • Viktor Zamaraev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)

Abstract

The Ramsey number \(R_X(p,q)\) for a class of graphs X is the minimum n such that every graph in X with at least n vertices has either a clique of size p or an independent set of size q. We say that Ramsey number is linear in X if there is a constant k such that \(R_{X}(p,q) \le k(p+q)\) for all pq. In the present paper we conjecture that Ramsey number is linear in X if and only if the co-chromatic number is bounded in X and determine Ramsey numbers for several classes of graphs that verify the conjecture.

Notes

Acknowledgment

Vadim Lozin acknowledges support from the Russian Science Foundation Grant No. 17-11-01336.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsLondon School of EconomicsLondonUK
  2. 2.University of WarwickCoventryUK
  3. 3.Lobachevsky State University of Nizhniy NovgorodNizhny NovgorodRussia
  4. 4.Department of Computer ScienceDurham UniversityDurhamUK

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