An improved upper bound on the length of the longest cycle of a supercritical random graph

Graeme Kemkes, Nicholas Wormald

We improve Luczak's upper bounds on the length of the longest cycle in the random graph G(n,M) in the "supercritical phase" where M=n/2+s and s=o(n) but n^{2/3}=o(s). The new upper…