Brooks proved that the chromatic number of a loopless connected graph G is at most the maximum degree of G unless G is an odd cycle or a clique. This note proves an analogue of this theorem for GF(p)-representable matroids when p is prime, thereby verifying a natural generalization of a conjecture of Peter Nelson.
Publication Source (Journal or Book title)
European Journal of Combinatorics
Oxley, J. (2016). A matroid analogue of a theorem of Brooks for graphs. European Journal of Combinatorics, 53, 45-49. https://doi.org/10.1016/j.ejc.2015.10.011