Minimum Cycle Decomposition: A Constructive Characterization for Graphs of Treewidth Two with Node Degrees Two and Four

TL;DR

This paper characterizes Eulerian graphs with treewidth 2 and maximum degree 4, providing a linear-time algorithm to compute the minimum cycle decomposition for this class.

Contribution

It offers a constructive characterization of a specific class of Eulerian graphs and an efficient algorithm to compute their minimum cycle decompositions.

Findings

Characterization of Eulerian graphs with treewidth 2 and degree 4

Linear-time algorithm for minimum cycle decomposition

Efficient computation for a specific graph class

Abstract

Substantial efforts have been made to compute or estimate the minimum number $c(G)$ of cycles needed to partition the edges of an Eulerian graph. We give an equivalent characterization of Eulerian graphs of treewidth $2$ and with maximum degree $4$. This characterization enables us to present a linear time algorithm for the computation of $c(G)$ for all $G$ in this class.