Hadwiger's Conjecture for inflations of 3-chromatic graphs

Hadwiger's Conjecture states that every k -chromatic graph has a complete minor of order k . A graph G ' is an inflation of a graph G if G ' is obtained from G by replacing each vertex v of G by a clique C v and joining two vertices of distinct cliques by an edge if and only if the corresponding vertices of G are adjacent. We present an algorithm for computing an upper bound on the chromatic number ? ( G ' ) of any inflation G ' of any 3 -chromatic graph G . As a consequence, we deduce that Hadwiger's Conjecture holds for any inflation of any 3 -colorable graph.

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