2002/12/04 by Péter Komjáth, Saharon Shelah, Komjáth, Péter +1
Computer Science · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.math/0212064
published as J. Graph Theory 49 No. 1 (2005) 28--38
arxiv created 2002/12/04 · openalex publication_date 2002/12/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is consistent that for every monotonically increasing function f:omega->omega there is a graph with size and chromatic number aleph1 in which every n-chromatic subgraph has at least f(n) elements (n >= 3). This solves a 250 problem of Erdos. It is also consistent that there is a graph X with Chr(X)=|X|= aleph1 such that if Y is a graph all whose finite subgraphs occur in X then Chr(Y)<=aleph2 (so the Taylor conjecture may fail).