Chromatic Number and the 2-Rank of a Graph

C.D. Godsil, Gordon F. Royle
2001 Journal of combinatorial theory. Series B (Print)  
We show that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2 r +1, and that this bound is tight.
doi:10.1006/jctb.2000.2003 fatcat:w2buzib4nbdltl5y2wwgm5bx7q