  The Conjecture of Hadwiger implies that the Hadwiger number $h$ times the
independence number $\alpha$ of a graph is at least the number of vertices $n$
of the graph. In 1982 Duchet and Meyniel proved a weak version of the
inequality, replacing the independence number $\alpha$ by $2\alpha-1$, that is,
$$(2\alpha-1)\cdot h \geq n.$$ In 2005 Kawarabayashi, Plummer and the second
author published an improvement of the theorem, replacing $2\alpha - 1$ by
$2\alpha - 3/2$ when $\alpha$ is at least 3. Since then a further improvement
by Kawarabayashi and Song has been obtained, replacing $2\alpha - 1$ by
$2\alpha - 2$ when $\alpha$ is at least 3.
  In this paper a basic elementary extension of the Theorem of Duchet and
Meyniel is presented. This may be of help to avoid dealing with basic cases
when looking for more substantial improvements. The main unsolved problem (due
to Seymour) is to improve, even just slightly, the theorem of Duchet and
Meyniel in the case when the independence number $\alpha$ is equal to 2. The
case $\alpha = 2$ of Hadwiger's Conjecture was first pointed out by Mader as an
interesting special case.
