Let M be a matroid representable over GF(q) and S be a subset of its ground set. In this note we prove that S is maximal with the property that the critical exponent c(M|S; q) does not exceed k if and only if S is maximal with the property that c(M · S) ≤ k. In addition, we show that, for regular matroids, the corresponding result holds for the chromatic number. © 1984, Academic Press Inc. (London) Limited. All rights reserved.
Publication Source (Journal or Book title)
European Journal of Combinatorics
Asano, T., Nishizeki, T., Saito, N., & Oxley, J. (1984). A Note on the Critical Problem for Matroids. European Journal of Combinatorics, 5 (2), 93-97. https://doi.org/10.1016/S0195-6698(84)80021-9