Ramsey numbers of ordered graphs

Martin Balko, Josef Cibulka, Karel Král, Jan Kynčl

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

An ordered graph is a graph together with a total ordering of its vertices. We study ordered Ramsey numbers, the analogue of Ramsey numbers for ordered graphs.In contrast with the case of unordered graphs, we show that there are ordered matchings whose ordered Ramsey numbers are super-polynomial in the number of vertices.We also prove that ordered Ramsey numbers are polynomial in the number of vertices of the given ordered graph G if G has constant degeneracy and constant interval chromatic number or if G has constant bandwidth. The latter result answers positively a question of Conlon, Fox, Lee, and Sudakov.For a few special classes of ordered graphs, we give asymptotically tight bounds for their ordered Ramsey numbers. For so-called monotone cycles we compute their ordered Ramsey numbers exactly.

Original languageEnglish
Pages (from-to)419-424
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume49
DOIs
StatePublished - 1 Nov 2015
Externally publishedYes

Keywords

  • Ordered Ramsey number
  • Ordered graph
  • Ramsey number

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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