# Graphs avoiding immersion of K_{3,3}

## TL;DR

This paper provides a simplified proof of the structural characterization of graphs that do not contain an immersion of K_{3,3}, showing they are constructed from small graphs and 3-regular planar graphs via small edge-cuts.

## Contribution

It offers an alternative, simpler proof of the known structural description of graphs avoiding an immersion of K_{3,3}.

## Key findings

- Graphs avoiding K_{3,3} immersion are composed from small graphs and 3-regular planar graphs.
- The proof simplifies understanding of the structure of such graphs.
- Supports the existing characterization with a more accessible proof.

## Abstract

DeVos and Malekian gave a structural description of graphs avoiding an immersion of K_{3,3}, showing that all such graphs are composed over small edge-cuts from graphs with at most 8 vertices and from 3-regular planar graphs. We provide another proof of this fact, simpler in some aspects.