Lower bounds of Ramsey numbers based on cubic residues (Q1613444)

New lower bounds for classical 2-colored Ramsey numbers \(r(k,l)\) are derived for small values of \(k\) and \(l\). In particular, previous bounds for \(k=5\) and \(l=15\), for \(k=6\) and \(l=12,14,\ldots,22\), for \(k=7\) and \(l=19,21\), for \(k=8\) and \(l=20,21\), and for \(k=9\) and \(l=20\) are improved. The lower bounds are based on a method for the construction of cyclic graphs based on cubic residues modulo prime numbers of the form \(p=6m+1\).