# Sh:788

- Komjáth, P., & Shelah, S. (2005).
*Finite subgraphs of uncountably chromatic graphs*. J. Graph Theory,**49**(1), 28–38. arXiv: math/0212064 DOI: 10.1002/jgt.20060 MR: 2130468 -
Abstract:

It is consistent that for every monotonically increasing function f:\omega\to\omega there is a graph with size and chromatic number \aleph_1 in which every n-chromatic subgraph has at least f(n) elements (n\geq 3). This solves a 250 problem of Erdős. It is also consistent that there is a graph X with {\rm Chr}(X)=|X|=\aleph_1 such that if Y is a graph all whose finite subgraphs occur in X then {\rm Chr}(Y)\leq \aleph_2. - Version 2002-05-24_11 (11p) published version (11p)

Bib entry

@article{Sh:788, author = {Komj{\'a}th, P{\'e}ter and Shelah, Saharon}, title = {{Finite subgraphs of uncountably chromatic graphs}}, journal = {J. Graph Theory}, fjournal = {Journal of Graph Theory}, volume = {49}, number = {1}, year = {2005}, pages = {28--38}, issn = {0364-9024}, mrnumber = {2130468}, mrclass = {05C15 (03E05 03E35)}, doi = {10.1002/jgt.20060}, note = {\href{https://arxiv.org/abs/math/0212064}{arXiv: math/0212064}}, arxiv_number = {math/0212064} }