EN|RU Volume 16, No 4, 2009, P. 87-96 UDC 519.1 P. V. Skums, R. I. Tyshkevich Reconstruction conjecture for graphs with restrictions for 4-vertex paths Abstract: The well-known Kelly–Ulam reconstruction conjecture is considered. It is proved that the conjecture holds for $P_4$-disconnected and $P_4$-tidy graphs. In particular, it generalizes the known results on the reconstructibility of disconnected graphs, complements of disconnected graphs, 1-decomposable graphs, and $P_4$-reducible graphs. Bibl. 19. Keywords: reconstruction conjecture, $P_4$-disconnected graphs, $P_4$-tidy graphs, $P_4$-reducible graphs, 1-decomposable graphs. Skums Pavel Valentinovich 1 Tyshkevich Regina Iosiphovna 1 1. Belarusian State University, 4 Nezavisimosti ave., 220030 Minsk, Belarus e-mail: skumsp@gmail.com, tyshkevich@bsu.by © Sobolev Institute of Mathematics, 2015