M-Convex Functions on Jump Systems: A General Framework for Minsquare Graph Factor Problem

Abstract

The concept of M-convex functions is generalized for functions defined on constant-parity jump systems. M-convex functions arise from minimumweight perfect b-matchings and from a separable convex function (sum of univariate convex functions) on the degree sequences of an undirected graph. As a generalization of a recent result of Apollonio and Sebo for the minsquare factor problem, a local optimality criterion is given for minimization of an M-convex function subject to a component sum constraint.