Degree-3 Planar Graphs as Topological Minors of Wall Graphs in Polynomial Time

TL;DR

This paper proves that degree-3 planar graphs can be efficiently embedded as topological minors within large wall graphs, providing a key step for a broader graph theory proof.

Contribution

It introduces a polynomial-time method to find degree-3 planar graphs as topological minors in large wall graphs, filling a gap in existing graph minor theory.

Findings

Efficient polynomial-time algorithm for embedding degree-3 planar graphs as topological minors.

Establishes a foundational step for further graph minor research.

Supports the proof of a larger theorem in graph theory.

Abstract

In this note, we give a proof of the fact that we can efficiently find degree-3 planar graphs as topological minors of sufficiently large wall graphs. The result is needed as an intermediate step to fix a proof in my PhD thesis.