Locally connected spanning trees on graphs

TL;DR

This paper presents linear-time algorithms for finding locally connected spanning trees specifically on strongly chordal graphs and proper circular-arc graphs, addressing a specialized graph problem.

Contribution

It introduces efficient algorithms for constructing locally connected spanning trees on two specific classes of graphs, expanding the toolkit for graph connectivity problems.

Findings

Linear-time algorithm for strongly chordal graphs

Linear-time algorithm for proper circular-arc graphs

Efficient solutions for a specialized spanning tree problem

Abstract

A locally connected spanning tree of a graph $G$ is a spanning tree $T$ of $G$ such that the set of all neighbors of $v$ in $T$ induces a connected subgraph of $G$ for every $v\in V(G)$. The purpose of this paper is to give linear-time algorithms for finding locally connected spanning trees on strongly chordal graphs and proper circular-arc graphs, respectively.