We prove the following recent conjecture of Halin. Let Gamma (0) be the cla
ss of all graphs, and for every ordinal mu > 0 let Gamma (mu), be the class
of all graphs containing infinitely many disjoint connected graphs from T-
lambda, for every lambda < <mu>. Then a graph lies in all these classes Gam
ma (mu) if and only if it contains a subdivision of the infinite binary tre
e. Published by John Wiley & Sons, Inc.