Edge connectivity in graphs: an expansion theorem

TL;DR

This paper proves an expansion theorem demonstrating that attaching a graph with certain diameter and degree conditions to a k-edge-connected graph preserves its edge connectivity.

Contribution

It introduces a new expansion theorem that guarantees the preservation of edge connectivity under specific graph attachment conditions.

Findings

Edge connectivity is preserved under certain graph expansions.

A new sufficient condition involving diameter and degree for connectivity preservation.

Theoretical framework for graph augmentation maintaining connectivity.

Abstract

We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting one graph to the other, the resulting graph is also k-edge-connected.