Some relations among term rank, clique number and list chromatic number of a graph Original Research Article

Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and term rank of G, by image and image, respectively. van Nuffelen conjectured that for any graph G, image. The first counterexample to this conjecture was obtained by Alon and Seymour. In 2002, Fishkind and Kotlov proved that for any graph G, image. Here we improve this upper bound and show that image, where image is the list chromatic number of G.