2022/10/06 by Johannes Carmesin, Carmesin, Johannes
Computer Science · Mathematics · #03E05 #05C10 #05C75 #05C83 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2210.02711
openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph H is ubiquitous if for every graph G that for every natural number n contains n vertex-disjoint H-minors contains infinitely many vertex-disjoint H-minors. Andreae conjectured that every locally finite graph is ubiquitous. We give a disconnected counterexample to this conjecture. It remains open whether every connected locally finite graph is ubiquitous.