Subcritical graph classes containing all planar graphs

TL;DR

This paper constructs specific graph families that include all planar graphs and are subcritical, challenging a longstanding conjecture in graph theory.

Contribution

It introduces minor-closed, addable, subcritical graph families that contain all planar graphs, providing a counterexample to a known conjecture.

Findings

Constructed minor-closed, addable, subcritical graph families

These families include all planar graphs

Contradict a well-known conjecture of Noy

Abstract

We construct minor-closed addable families of graphs that are subcritical and contain all planar graphs. This contradicts (one direction of) a well-known conjecture of Noy.