Seymour and Woodall's conjecture holds for graphs with independence number two

Woodall (and Seymour independently) in 2001 proposed a conjecture that every graph G contains every complete bipartite graph on (G) vertices as a minor, where (G) is the chromatic number of G. In this paper, we prove that for each positive integer with 2 (G), each graph G with independence number two contains a K^, (₆) --minor, implying that Seymour and Woodall's conjecture holds for graphs with independence number two, where K^, (₆) - is the graph obtained from K, (₆) - by making every pair of vertices on the side of the bipartition of size adjacent.