Published online by Cambridge University Press: 06 April 2021
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).
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).