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math.CO2018
Online Ramsey Numbers and the Subgraph Query Problem
David Conlon, Jacob Fox, Andrey Grinshpun +1
The -online Ramsey game is a combinatorial game between two players, Builder and Painter. Starting from an infinite set of isolated vertices, Builder draws an edge on each t…
math.CO2015
On the minimum degree of minimal Ramsey graphs for multiple colours
Jacob Fox, Andrey Grinshpun, Anita Liebenau +2
A graph G is r-Ramsey for a graph H, denoted by G\rightarrow (H)_r, if every r-colouring of the edges of G contains a monochromatic copy of H. The graph G is called r-Ramsey-minima…
math.CO2013
The Erdős-Hajnal conjecture for rainbow triangles
J. Fox, A. Grinshpun, J. Pach
We prove that every 3-coloring of the edges of the complete graph on n vertices without a rainbow triangle contains a set of order Omega(n^{1/3}log^2 n) which uses at most two colo…