On Off-Diagonal Ordered Ramsey Numbers of Nested Matchings

Martin Balko, Marian Poljak

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

For two ordered graphs G< and H<, the ordered Ramsey number r<(G<, H<) is the minimum N such that every red-blue coloring of the edges of the ordered complete graph KN< contains a red copy of G< or a blue copy of H<. For n∈ N, a nested matching NMn< is the ordered graph on 2n vertices with edges { i, 2 n- i+ 1 } for every i= 1, ⋯, n. We improve bounds on the numbers r<(NMn<,K3<) obtained by Rohatgi, we disprove his conjecture about these numbers, and we determine them exactly for n= 4, 5. This gives a stronger lower bound on the maximum chromatic number of k-queue graphs for every k≥ 3. We expand the classical notion of Ramsey goodness to the ordered case and we attempt to characterize all connected ordered graphs that are n-good for every n∈ N. In particular, we discover a new class of such ordered trees, extending all previously known examples.

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages241-247
Number of pages7
DOIs
StatePublished - 1 Jan 2021
Externally publishedYes

Publication series

NameTrends in Mathematics
Volume14
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Keywords

  • Nested matching
  • Ordered Ramsey number
  • Ramsey goodness

ASJC Scopus subject areas

  • General Mathematics

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