The complement of a nIL graph with thirteen vertices is IL

TL;DR

This paper proves that for any simple non-oriented graph with thirteen or more vertices, either the graph itself or its complement contains an intrinsically linked subgraph, advancing understanding of graph linking properties.

Contribution

It establishes a new threshold for intrinsic linking in graphs, showing the complement of a 13-vertex graph also exhibits this property.

Findings

Graphs with at least thirteen vertices are intrinsically linked or their complements are.

The complement of a 13-vertex graph is also intrinsically linked.

This result extends previous knowledge on intrinsic linking thresholds.

Abstract

We show that for any simple non-oriented graph G with at least thirteen vertices either G or its complement is intrinsically linked.