Ramsey Theory Check

So, I want to create a program that would check if a graph contains a complete sub-graph (more in the Party Problem) and my point is to prove that the computer fails to do so quickly as the number of graph’s vertices increase. So far, I have come up with only this code, but it doesn’t work for some reason. Any suggestions?

   RamseyNumber[k_, l_] := Module[{i = 3, r = 0},   While[    i <= Length[list] && r == 0,    If[((#[[1]] >= k || #[[2]] >= l) & /@       (And @@ list[[i]])), r = i, i++]    ]; r   ]  RamseyNumber[n_] := RamseyNumber[n, n]  Timing[  in = Table[     Length /@ MaximumIndependentSet /@ Graphs[n], {n, 8}     ];  ]