An infinite family of linklessly embeddable Tutte-4-connected graphs

TL;DR

This paper constructs an infinite family of large, highly connected graphs that can be embedded in three-dimensional space without links, advancing understanding of graph embeddings and topological graph theory.

Contribution

It introduces a new infinite family of linklessly embeddable, Tutte-4-connected graphs for all sufficiently large sizes, filling a gap in graph embedding theory.

Findings

Existence of such graphs for all n ≥ 14

Graphs are Tutte-4-connected and linklessly embeddable

Provides explicit examples for each size n ≥ 14

Abstract

For each $n\ge 14$, we provide an example of a linklessly embeddable, Tutte-4-connected graph of order $n$.