Hadwiger's Conjecture is True for Almost Every Graph
The contraction clique number ccl(G) of a graph G is the maximal r for which G has a subcontraction to the complete graph K′. We prove that for d > 2, almost every graph of order n satisfies n((log2n)1/2+4)-1 ⩽ ccl(G) ⩽ n(log2n-d log2 log2n)1/2. This inequality implies the statement in the title. © 1980, Academic Press Inc. (London) Limited. All rights reserved.
European Journal of Combinatorics
Bollobás, B., Catlin, P., & Erdös, P. (1980). Hadwiger's Conjecture is True for Almost Every Graph. European Journal of Combinatorics, 1 (3), 195-199. https://doi.org/10.1016/S0195-6698(80)80001-1