On some extremal connectivity results for graphs and matroids
Dirac and Halin have shown for n = 2 and n = 3 respectively that a minimally n-connected graph G has at least ((n-1)|V(G)|-2n)/(2n-1) vertices of degree n. This paper determines the graphs which are extremal with respect to these two results and, in addition, establishes a similar extremal result for minimally connected matroids. © 1982.
Publication Source (Journal or Book title)
Oxley, J. (1982). On some extremal connectivity results for graphs and matroids. Discrete Mathematics, 41 (2), 181-198. https://doi.org/10.1016/0012-365X(82)90206-0