Volume 16, No 4, 2009, P. 87-96
P. V. Skums, R. I. Tyshkevich
Reconstruction conjecture for graphs with restrictions for 4-vertex paths
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.
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: firstname.lastname@example.org, email@example.com