An Upper Bound of 7n/6 for the Minimum Size 2EC on Cubic 3-Edge Connected Graphs

TL;DR

This paper establishes a new upper bound of 7n/6 for the size of minimum 2-edge connected spanning subgraphs in cubic 3-edge connected graphs, improving previous bounds.

Contribution

The paper proves a tighter upper bound of 7n/6 for 2EC in cubic 3-edge connected graphs, advancing the understanding of graph connectivity constraints.

Findings

New upper bound of 7n/6 for 2EC in cubic 3-edge connected graphs

Improvement over previous bound of 6n/5

Enhanced theoretical understanding of graph connectivity

Abstract

In this paper, we study the minimum size 2-edge connected spanning subgraph problem (henceforth 2EC) and show that every 3-edge connected cubic graph G=(V, E), with n=|V| allows a 2EC solution for G of size at most 7n/6, which improves upon Boyd, Iwata and Takazawa's guarantee of 6n/5.