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arXiv math/02120642002-12-04math.LO

Finite subgraphs of uncountably chromatic graphs

Péter Komjáth, Saharon Shelah

发表信息：: J. Graph Theory 49 No. 1 (2005) 28--38

英文摘要：

It is consistent that for every monotonically increasing function f:omega->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 >= 3). This solves a $250 problem of Erdos. It is also consistent that there is a graph X with Chr(X)=|X|= aleph_1 such that if Y is a graph all whose finite subgraphs occur in X then Chr(Y)<=aleph_2 (so the Taylor conjecture may fail).

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