On the Numbers of Bases and Circuits in Simple Binary Matroids
Quirk and Seymour have shown that a connected simple graph has at least as many spanning trees as circuits. This paper extends and strengthens their result by showing that in a simple binary matroid M the quotient of the number of bases by the number of circuits is at least 2. Moreover, if M has no coloops and rank r, this quotient exceeds 6(r + 1)/19. © 1983, Academic Press Inc. (London) Limited. All rights reserved.
Publication Source (Journal or Book title)
European Journal of Combinatorics
Oxley, J. (1983). On the Numbers of Bases and Circuits in Simple Binary Matroids. European Journal of Combinatorics, 4 (2), 169-178. https://doi.org/10.1016/S0195-6698(83)80047-X