The size-Ramsey number of short subdivisions

Nemanja Draganić, Michael Krivelevich, Rajko Nenadov

Research output: Contribution to journalArticlepeer-review

Abstract

The r-size-Ramsey number (Formula presented.) of a graph H is the smallest number of edges a graph G can have such that for every edge-coloring of G with r colors there exists a monochromatic copy of H in G. For a graph H, we denote by Hq the graph obtained from H by subdividing its edges with q − 1 vertices each. In a recent paper of Kohayakawa, Retter and Rödl, it is shown that for all constant integers q, r ≥ 2 and every graph H on n vertices and of bounded maximum degree, the r-size-Ramsey number of Hq is at most (Formula presented.), for n large enough. We improve upon this result using a significantly shorter argument by showing that (Formula presented.) for any such graph H.

Original languageEnglish
Pages (from-to)68-78
Number of pages11
JournalRandom Structures and Algorithms
Volume59
Issue number1
DOIs
StatePublished - Aug 2021

Keywords

  • Ramsey theory
  • random graphs
  • subdivisions

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