Problem
COM-B2-M06-P015 A Bound for \(R(4,4)\)
#15
★★★★☆ Level 4 of 5
Using \(R(3,4)\le10\), prove that \(R(4,4)\le20\).
Apply the recursion to \(R(4,4)\).
By Ramsey recursion,
\[R(4,4)\le R(3,4)+R(4,3).\]
By symmetry, \(R(4,3)=R(3,4)\). Since \(R(3,4)\le10\), we obtain
\[R(4,4)\le10+10=20.\]
The problem shows how larger bounds are built from smaller ones.