A tree--arrowing graph

by Milner and Shelah. [MlSh:578]
Set Theory: Techniques and Applications, (J. Bagaria, C. Di Prisco, J. Larson, A.R.D. Mathias, eds.), 1998
We answer a variant of a question of R{o}dl 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.

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