Hadwiger's Conjecture is True for Almost Every Graph

Authors

B. Bollobás, Faculty of MathematicsFollow
P. A. Catlin, Wayne State UniversityFollow
P. Erdös, Alfréd Rényi Institute of Mathematics

Abstract

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.

Publication Title

European Journal of Combinatorics

Recommended Citation

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