Optimal Kₜ-free list colorings and the Pollyanna property of graphs with no triangular wheel

A wheel consists of an induced cycle of length at least four and a vertex with at least three neighbors on the cycle. Let T be the class of graphs with no wheel containing a triangle. We prove that, for every G∈ T and every integer t≥3, the Kₜ-free chromatic and choice numbers both equal ω(G)/(t-1). We further prove that T is k-strongly linear-Pollyanna for every integer k≥2, and hence is linear-Pollyanna. In particular, the class of wheel-free graphs is Pollyanna, answering Problem 10.2 of Chudnovsky, Cook, Davies and Oum.