Hadwiger Number and the Cartesian Product of Graphs

摘要

The Hadwiger number η(G) of a graph G is the largest integer n for which the complete graph K n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, η(G) ≥ χ(G), where χ(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product $G square H$ of graphs.