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On the size-Ramsey number of grid graphs

Part of: Extremal combinatorics

Published online by Cambridge University Press:  06 April 2021

Dennis Clemens ,
Meysam Miralaei ,
Damian Reding ,
Mathias Schacht  and
Anusch Taraz
Dennis Clemens
Affiliation:
Institut für Mathematik, TU Hamburg, Hamburg, Germany
Meysam Miralaei
Affiliation:
Department of Mathematics, Isfahan University of Technology, Isfahan, Iran
Damian Reding
Affiliation:
Institut für Mathematik, TU Hamburg, Hamburg, Germany
Mathias Schacht*
Affiliation:
Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany
Anusch Taraz
Affiliation:
Institut für Mathematik, TU Hamburg, Hamburg, Germany
*
*Corresponding author. Email: schacht@math.uni-hamburg.de
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Abstract

The size-Ramsey number of a graph F is the smallest number of edges in a graph G with the Ramsey property for F, that is, with the property that any 2-colouring of the edges of G contains a monochromatic copy of F. We prove that the size-Ramsey number of the grid graph on n × n vertices is bounded from above by n3+o(1).

MSC classification

Primary: 05D10: Ramsey theory
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 5 , September 2021 , pp. 670 - 685
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

M. Miralaei was supported by the Ministry of Science, Research and Technology of Iran and part of the research was carried out during a visit to the University of Hamburg.

‡

M. Schacht was partly supported by the European Research Council (PEPCo 724903).

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