Low-degree spanning trees of $2$-edge-connected graphs in linear time

TL;DR

This paper introduces a linear-time algorithm for constructing a spanning tree in 2-edge-connected graphs where each vertex's degree is bounded by roughly half its original degree, optimizing the tree structure efficiently.

Contribution

The paper presents a novel linear-time algorithm for finding low-degree spanning trees in 2-edge-connected graphs, improving efficiency and degree bounds.

Findings

Algorithm runs in linear time.

Constructs spanning trees with degree at most half of original plus one.

Applicable to 2-edge-connected graphs.

Abstract

We present a simple linear-time algorithm that finds a spanning tree $T$ of a given $2$-edge-connected graph $G$ such that each vertex $v$ of $T$ has degree at most $\lceil \frac{\deg_G(v)}{2}\rceil + 1$.