On the size-Ramsey number of grids
David Conlon, Rajko Nenadov, and Milo\v{s} Truji\'c

TL;DR
This paper establishes an improved upper bound on the size-Ramsey number of grid graphs, demonstrating that it grows at most as fast as O(n^{5/4}), which advances previous bounds significantly.
Contribution
The authors provide a tighter upper bound on the size-Ramsey number of grid graphs, improving upon earlier results by refining the growth rate to O(n^{5/4}).
Findings
Size-Ramsey number of the grid is O(n^{5/4})
Improves previous bound of n^{3/2 + o(1)}
Advances understanding of Ramsey properties of grid graphs
Abstract
We show that the size-Ramsey number of the grid graph is , improving a previous bound of by Clemens, Miralaei, Reding, Schacht, and Taraz.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Computational Geometry and Mesh Generation · Complexity and Algorithms in Graphs
