A synthesis for exactly 3-edge-connected graphs

TL;DR

This paper characterizes and provides a constructive synthesis for exactly 3-edge-connected graphs, including planar and minimal-edge variants, advancing understanding of their structure and generation.

Contribution

It introduces a novel synthesis method using two operations to generate all exactly 3-edge-connected multigraphs, including special subclasses.

Findings

Characterization of exactly 3-edge-connected graphs

Synthesis operations for graph generation

Extensions to planar and minimal-edge graphs

Abstract

A multigraph is exactly k-edge-connected if there are exactly k edge-disjoint paths between any pair of vertices. We characterize the class of exactly 3-edge-connected graphs, giving a synthesis involving two operations by which every exactly 3-edge-connected multigraph can be generated. Slightly modified syntheses give the planar exactly 3-edge-connected graphs and the exactly 3-edge-connected graphs with the fewest possible edges.