Consistency results on infinite graphs
- 63 Downloads
Consistently there exist ℵ2-chromatic graphs with no ℵ1-chromatic subgraphs. The statement that every uncountably chromatic graph of size ℵ1 contains an uncountably chromaticω-connected subgraph is consistent and independent. It is consistent that there is an uncountably chromatic graph of size ℵω 1 in which every subgraph with size less than ℵω 1 is countably chromatic.
Unable to display preview. Download preview PDF.
- 2.W. W. Comfort and S. Negrepontis,Chain Conditions in Topology, Cambridge University Press, 1982.Google Scholar
- 3.P. Erdös,Problems and results on finite and infinite combinatorial analysis, inInfinite and Finite Sets, Coll. Math. Soc. J. Bolyai, 10 (A. Hajnal, R. Rado and V. T. Sós, eds.), pp. 403–424.Google Scholar
- 6.P. Erdös,Problems and results on chromatic numbers in finite and infinite graphs, inGraph Theory with Applications to Algorithms and Computer Science (Y. Alavi, G. Chartrand, L. Lesniak, D. R. Lich and C. E. Wall, eds.), John Wiley and Sons, 1985, pp. 201–213.Google Scholar
- 10.M. Foreman and R. Laver,A graph transfer property, to appear.Google Scholar
- 13.P. Komjáth and S. Shelah,Forcing constructions for uncountable chromatic graphs, J. Symb. Logic, to appear.Google Scholar
- 14.S. Shelah,Remarks on cardinal invariants in topology, Gen. Topol. Appl.7 (1977), 251–259.Google Scholar