A theory of “discrete convex analysis” is developed for integer-valued functions defined on
integer lattice points. The theory parallels the ordinary convex analysis, covering discrete …

This paper describes recent developments in discrete convex analysis. Particular emphasis
is laid on natural introduction of the classes of L-convex and M-convex functions in discrete …

Discrete convex functions are used in many areas, including operations research, discrete-
event systems, game theory, and economics. The objective of this paper is to offer a survey …

We consider the problem of making a given (k− 1)-connected graph k-connected by adding
a minimum number of new edges, which we call the k-connectivity augmentation problem. In …

We present a min-max formula and a polynomial time algorithm for a slight generalization of
the following problem: in a simple undirected graph in which the degree of each node is at …

Discrete convex functions are used in many areas, including operations research, discrete-
event systems, game theory, and economics. The objective of this paper is to investigate …

In this paper, we consider the problem of finding a maximum weight 2-matching containing
no cycle of a length of at most three in a weighted simple graph, which we call the weighted …

For an undirected graph and a fixed integer k, a 2-matching is said to be k-restricted if it has
no cycle of length k or less. The problem of finding a maximum cardinality k-restricted 2 …

Given a digraph G=(VG, AG), an even factor M⊆ AG is a set formed by node-disjoint paths
and even cycles. Even factors in digraphs were introduced by Geelen and Cunningham and …

We propose a new framework of optimal t-matchings excluding prescribed t-factors in
bipartite graphs. It is a generalization of the nonbipartite matching problem and includes a …