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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 rk(G) and Rk(G), respectively. van Nuffelen conjectured that for any graph G, χ(G)⩽rk(G). The first counterexample to this conjecture was obtained by Alon and Seymour. In 2002, Fishkind and Kotlov proved that for any graph G, χ(G)⩽Rk(G). Here we improve this upper bound and show that χl(G)⩽(rk(G)+Rk(G))/2,...
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