Hadwiger's Conjecture for some graphs with independence number two

Let h(G) denote the largest t such that G contains K_t as a minor and χ(G) be the chromatic number of G respectively. In 1943, Hadwiger conjectured that h(G) ≥χ(G) for any graph G. In this paper, we prove that Hadwiger's conjecture holds for H-free graphs with independence number two, where H is one of some specified graphs.