Depth-first search in split-by-edges trees

TL;DR

This paper investigates depth-first search strategies in split-by-edges trees for graphs, highlighting their efficiency and oscillating success rates in finding independent sets, with implications for graph algorithms.

Contribution

It introduces analysis of depth-first search performance in split-by-edges trees, emphasizing oscillating success rates and potential algorithmic insights.

Findings

Depth-first search runs in linear time in split-by-edges trees.

Success rate oscillates significantly with graph size.

Potential for improved algorithms based on oscillation patterns.

Abstract

A layerwise search in a split-by-edges tree (as defined by Br{\ae}ndeland, 2015) of agiven graph produces a maximum independent set in exponential time. A depth-first search produces an independent set, which may or may not be a maximum, in linear time, but the worst case success rate is maybe not high enough to make it really interesting. What may make depth-first searching in split-by-edges trees interesting, though, is the pronounced oscillation of its success rate along the graph size axis.