Universal graphs with forbidden wheel minors

TL;DR

This paper proves the existence of a universal graph within the class of countable graphs excluding a wheel minor, meaning it contains every such graph as an induced subgraph, advancing understanding of graph minors and universality.

Contribution

It establishes the existence of a universal graph for the class of countable wheel-minor-free graphs, a significant extension in the theory of graph minors and universality.

Findings

Existence of a universal graph in the class of wheel-minor-free graphs.

Universal graph contains all graphs in the class as induced subgraphs.

Advances understanding of structure and universality in minor-closed graph classes.

Abstract

Let $W$ be any wheel graph and $\mathcal{G}$ the class of all countable graphs not containing $W$ as a minor. We show that there exists a graph in $\mathcal{G}$ which contains every graph in $\mathcal{G}$ as an induced subgraph.