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Abstract
It is consistent that there exists an uncountably chromatic triple system which does not contain two triples with two common points or circuits of lengths 3, 5.
Acta Mathematica Hungarica
Authors:
A. Hajnal
and
P. Komjáth
Abstract
We determine a class of triple systems such that each must occur in a triple system with uncountable chromatic number that
omits \documentclass{aastex}
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$$\mathcal{T}_0$$
\end{document} (the unique system consisting of two triples on four vertices). This class contains all odd circuits of length ≧ 7. We also
show that consistently there are two finite triple systems such that they can separately be omitted by uncountably chromatic
triple systems but not both.
Periodica Mathematica Hungarica
Authors:
P. Komjáth
and
S. Shelah
It is consistent that there exists a set mappingF with ß<F(ß, a)<a for ß + 2 = a >w 2 with no uncountable free sets.
Page:12