Partial Result on Hadwiger's Conjecture

Let D = (d1, d2, …, dn) be a graphic sequence with 0 ≤ d1 ≤ d2 ≤ ⋯ ≤ dn. Any simple graph G with D its degree sequence is called a realization of D. Let R[D] denote the set of all realizations of D. We say that D is H-free if no graph in R[D] contains H as an induced subgraph. In this paper, we prove that Hadwiger's Conjecture is true for graphs whose degree sequences are claw-free or -free.