Some extremal connectivity results for matroids
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, we prove that every n-element subset X of E(M) is in an (n + 1)-element circuit if and only if (i) for every such subset, M X is disconnected, and (ii) for every subset Y with at most n elements, M Y is connected. Various extensions and consequences of this result are also derived including characterizations in terms of connectivity of the 4-point line and of Murty's Sylvester matroids. The former is a result of Seymour. © 1991.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory, Series B
Akkari, S., & Oxley, J. (1991). Some extremal connectivity results for matroids. Journal of Combinatorial Theory, Series B, 52 (2), 301-320. https://doi.org/10.1016/0095-8956(91)90070-Z