  This is a note on three graph parameters motivated by the Euler-Poincare
characteristic for simplicial complex. We show those three graph parameters of
a given connected graph $G$ is greater than or equal to that of the complete
graph with $\max(h(G),\chi(G))$ vertices. This will yield three different
simultaneous upperbounds of both the hadwiger number and chromatic number by
means of the number of particular types of induced subgraphs. Some applications
to Hadwiger's Conjecture is also discussed.
