# Sh:578

• Milner, E. C., & Shelah, S. (1998). A tree-arrowing graph. In Set theory (Curaçao, 1995; Barcelona, 1996), Kluwer Acad. Publ., Dordrecht, pp. 175–182.
• Abstract:
We answer a variant of a question of Rödl and Voigt by showing that, for a given infinite cardinal \lambda, there is a graph G of cardinality \kappa=(2^\lambda)^+ such that for any colouring of the edges of G with \lambda colours, there is an induced copy of the \kappa-tree in G in the set theoretic sense with all edges having the same colour.
• Version 1997-08-27_11 (9p) published version (8p)
Bib entry
@incollection{Sh:578,
author = {Milner, Eric Charles and Shelah, Saharon},
title = {{A tree-arrowing graph}},
booktitle = {{Set theory (Cura\c{c}ao, 1995; Barcelona, 1996)}},
year = {1998},
pages = {175--182},
publisher = {Kluwer Acad. Publ., Dordrecht},
mrnumber = {1602000},
mrclass = {03E05 (05C15)},
note = {\href{https://arxiv.org/abs/math/9708210}{arXiv: math/9708210}},
arxiv_number = {math/9708210}
}