Computational Lower Bounds for Wheel Ramsey Numbers

We study small off-diagonal Ramsey numbers involving wheel graphs. Following Radziszowski’s convention, we write $W_n=K_1+C_{n-1}$ for the wheel on n vertices. A lower bound for $R(W_m,W_n)$ is certified by a graph G such that G is $W_m$-free and $\overline{G}$ is $W_n$-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 $W_n$ if and only if some vertex neighborhood contains a cycle $C_{n-1}$. We report new lower-bound constructions for three off-diagonal wheel Ramsey numbers and provide the corresponding Ramsey graphs as explicit certificates.