Strong subgraph $k$-arc-connectivity

TL;DR

This paper introduces and analyzes the strong subgraph k-arc-connectivity of digraphs, providing characterizations, bounds, and complexity results, expanding the understanding of connectivity parameters in directed graphs.

Contribution

It defines the new parameter of strong subgraph k-arc-connectivity and offers foundational theoretical results, including characterizations and bounds, distinct from previous work on k-connectivity.

Findings

Established characterizations of the new parameter

Derived lower and upper bounds for strong subgraph k-arc-connectivity

Analyzed computational complexity of related problems

Abstract

Two previous papers, arXiv:1803.00284 and arXiv:1803.00281, introduced and studied strong subgraph $k$-connectivity of digraphs obtaining characterizations, lower and upper bounds and computational complexity results for the new digraph parameter. The parameter is an analog of well-studied generalized $k$-connectivity of undirected graphs. In this paper, we introduce the concept of strong subgraph $k$-arc-connectivity of digraphs, which is an analog of generalized $k$-edge-connectivity of undirected graphs. We also obtain characterizations, lower and upper bounds and computational complexity results for this digraph parameter. Several of our results differ from those obtained for strong subgraph $k$-connectivity.