The $K_{n+5}$ and $K_{3^2,1^n}$ families are obstructions to $n$-apex

TL;DR

This paper investigates specific graph families, $K_{n+5}$ and $K_{3^2,1^n}$, providing evidence that they serve as obstructions to the property of being $n$-apex, which relates to graph simplification.

Contribution

It offers evidence supporting the conjecture that these graph families are obstructions to the $n$-apex property, advancing understanding of graph minor theory.

Findings

Evidence supporting the conjecture for these graph families.

Identification of these families as obstructions to $n$-apex.

Contributes to the theory of graph minors and obstructions.

Abstract

We give evidence in support of a conjecture that the $\nabla$Y$\nabla$ families of $K_{n+5}$ and $K_{3^2,1^n}$ are obstructions for the $n$-apex property.