Subgraphs of 4-regular planar graphs

TL;DR

This paper introduces an algorithm to determine if a given planar graph can be embedded as a subgraph within a 4-regular planar graph, with applications to constructing such graphs when possible.

Contribution

It presents a novel algorithm with O(|H|^{2.5}) complexity for identifying and constructing 4-regular planar supergraphs containing a specified subgraph.

Findings

Algorithm can determine subgraph inclusion efficiently

Can construct explicit 4-regular planar graphs containing H

Works for simple graphs and multigraphs

Abstract

We shall present an algorithm for determining whether or not a given planar graph H can ever be a subgraph of a 4-regular planar graph. The algorithm has running time O(|H|^{2.5}) and can be used to find an explicit 4-regular planar graph G containing H if such a graph exists. It shall not matter whether we specify that H and G must be simple graphs or allow them to be multigraphs.