2-connecting Outerplanar Graphs without Blowing Up the Pathwidth

TL;DR

This paper presents an algorithm to augment connected outerplanar graphs to be 2-vertex-connected while preserving their outerplanar structure and pathwidth, addressing an open problem related to graph drawing.

Contribution

It provides the first efficient method to connect outerplanar graphs without increasing their pathwidth, enabling broader applications in graph drawing algorithms.

Findings

Algorithm successfully adds edges to achieve 2-vertex connectivity

Maintains outerplanarity and bounded pathwidth after augmentation

Enables constant factor approximation for minimum height drawings

Abstract

Given a connected outerplanar graph G of pathwidth p, we give an algorithm to add edges to G to get a supergraph of G, which is 2-vertex-connected, outerplanar and of pathwidth O(p). This settles an open problem raised by Biedl, in the context of computing minimum height planar straight line drawings of outerplanar graphs, with their vertices placed on a two dimensional grid. In conjunction with the result of this paper, the constant factor approximation algorithm for this problem obtained by Biedl for 2-vertex-connected outerplanar graphs will work for all outer planar graphs.