2022/03/23 by Thilo Krill, Krill, Thilo
Computer Science · Mathematics · #05C63 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2203.12643
openalex publication_date 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subgraph-universal graph/a topological minor-universal graph in a class of graphs G is a graph in G which contains every graph in G as a subgraph/topological minor. We prove that the class P of all countable planar graphs does not contain a topological minor-universal graph. This answers a question of Diestel and Kühn and strengthens a result of Pach stating that there is no subgraph-universal graph in P. Furthermore, we characterise for which subdivided stars T there is a topological minor-universal graph in the class of all countable T-free graphs.