The structure of decomposition of a triconnected graph

TL;DR

This paper analyzes the structure of triconnected graphs by decomposing them into small, well-structured groups called complexes, and introduces a hypertree structure to describe their arrangement comprehensively.

Contribution

It introduces a novel decomposition of triconnected graphs into complexes and establishes a hypertree framework to understand their relative structure.

Findings

Decomposition of all 3-cutsets into small complexes.

Introduction of a hypertree structure on complexes.

Complete description of complexes' relative disposition.

Abstract

We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a simple structure, named complexes. The detailed description of all complexes is presented. Moreover, we prove that the structure of a hypertree could be introduced on the set of all complexes. This structure gives us a complete description of the relative disposition of the complexes. Keywords: connectivity, triconneted graphs.