@article{Kawarabayashi2007IndependenceNA,
title={Independence number and clique minors},
author={Ken-ichi Kawarabayashi and Zi-Xia Song},
journal={Journal of Graph Theory},
year={2007},
volume={56},
pages={219-226}
}

Since χ(G) · α(G) ≥ |V (G)|, Hadwiger’s Conjecture implies that any graph G has the complete graph Kdn α e as a minor, where n is the number of vertices of G and α is the maximum number of independent vertices in G. Motivated by this fact, it is shown that any graph on n vertices with independence number α ≥ 3 has the complete graph Kd n 2α−2 e as a minor. This improves the well-known theorem of Duchet and Meyniel and the recent improvement due to Kawarabayashi, Plummer, Toft. A new result on… CONTINUE READING