We study small off-diagonal Ramsey numbers involving wheel graphs. Following Radziszowski’s convention, we write Wn=K1+Cn−1 for the wheel on n vertices. A lower bound for R(Wm,Wn) is certified by a graph G such that G is Wm-free and G¯ is Wn-free. We conduct computational experiments using several complementary search techniques, including partial Ramsey colorings and local search procedures. The computations exploit the structure of wheels: G contains Wn if and only if some vertex neighborhood contains a cycle Cn−1. We report new lower-bound constructions for three off-diagonal wheel Ramsey numbers and provide the corresponding Ramsey graphs as explicit certificates.
Sergey Bereg (Tue,) studied this question.