Prove or disprove that in any infinite list of graphs, some graph is a subdivision of another. **Problem** Prove or disprove that in any infinite list of graphs, some graph is a subdivision of another. **My idea** The graph minor theorem was proved by Robertson and Seymour in 1985, but I wonder if there is some counterexample to the analogue of subdivision.

In order to be a subdivision (of anything other than itself) a graph must have at least one vertex of degree $2$. So for any infinite list of graphs without vertices of degree $2$, no graph is a subdivision of any other.