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Is it true that if $G$ has $m$ edges then \[R(G) \leq 2^{O(m^{1/2})}?\]
#546
:
[Er84e]
graph theory
,
ramsey theory
This is true, and was proved by Sudakov
[Su11]
. The analogous question for $\geq 3$ colours is still open.
This problem is
#11 in Ramsey Theory
in the graphs problem collection.
Additional thanks to
: Zach Hunter
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