A set of vertices X of a graph G is convex if no shortest path between two vertices in X contains a vertex outside X. We prove that for fixed p >= 1, all partitions of the vertex set of a bipartite graph into p convex sets ...

We present some complexity results concerning the problems of covering a graph with p convex sets and of partitioning a graph into p convex sets. The following convexities are considered: digital convexity, monophonic ...

In this work we give an extension of the Brondsted-Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous epi-pointed functions defined in locally convex spaces. We use a new ...

We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that ...

In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level of generality among ...