An accessibility theorem for infinite graph minors

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.