2018•Mathematics of Operations ResearchRequires access

Supermodularity in Unweighted Graph Optimization III: Highly Connected Digraphs

Kristóf Bérczi, András Frank

Abstract

By generalizing a recent result of Hong, Liu and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple k-node-connected digraphs. More generally, we solve the directed node-connectivity augmentation problem when the augmented digraph is degree-specified and simple. As for edge-connectivity augmentation, we solve the special case when the edge-connectivity is to be increased by one and the augmenting digraph must be simple.

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Key concepts: Digraph, Simple (philosophy), Mathematics, Combinatorics, Degree (music), Node (physics), Strongly connected component, Directed graph