EN|RU Volume 15, No 5, 2008, P. 61-75 UDC 519.101 P. V. Salimov Existence of an infinite word with a rauzy graph sequence that contains a subsequence of homeomorphs of graphs of the given sequence Abstract: We investigate infinite words on a finite alphabet and prove that for any sequence of strongly connected directed graphs with maximal in and out vertices degrees that are equal to $s$ there exists a uniformly recurrent infinite word on a $s$-letters alphabet with a Rauzy graph sequence that contains a subsequence of homeomorphs of graphs of the given sequence.  Bibl. 5. Keywords: infinite words, uniform reccurancy, Rauzy graph, de Brain graphs. Salimov Pavel Vadimovich 1 1. S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia e-mail: ch.cat.s.smile@gmail.com © Sobolev Institute of Mathematics, 2015