A complete description of convex sets associated with matchings and edge-connectivity in graphs

Let (Formula presented.) be the set of pairs (Formula presented.) of real numbers with the property there exists a constant (Formula presented.), depending only on (Formula presented.) and (Formula presented.), such that (Formula presented.) for every connected graph (Formula presented.) of order (Formula presented.), size (Formula presented.), with maximum degree at most (Formula presented.) and edge-connectivity at least (Formula presented.). In a recent paper, the authors give a complete description of the set (Formula presented.). In this article we raise the problem to a higher level, and give a complete description of the convex set (Formula presented.) for all (Formula presented.), and determine its extreme points.