About reconstruction of small tournaments
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 94-98
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A tournament of ordernis a complete graph of $n$ nodes with each arc assigned a unique direction. The reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. This conjecture was proved to be false when P. K. Stockmeyer discovered several infinite families of counterexample pairs of digraphs (including tournaments). In this paper we observe known results about reconstruction of tournaments and present our approach to study reconstruction of all tournaments with up to 12 vertexes.
@article{ISU_2009_9_2_a14,
author = {M. B. Abrosimov and A. A. Dolgov},
title = {About reconstruction of small tournaments},
journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
pages = {94--98},
year = {2009},
volume = {9},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a14/}
}
M. B. Abrosimov; A. A. Dolgov. About reconstruction of small tournaments. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 94-98. http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a14/
[1] Bogomolov A. M., Salii V. N., Algebraicheskie osnovy teorii diskretnykh sistem, Nauka, M., 1997 | MR | Zbl
[2] Kharari F., Teoriya grafov, URSS, M., 2003
[3] Stockmeyer P., “My quest for non-reconstructable graphs”, Congressus Numerantium, 63 (1988), 188–200 | MR | Zbl
[4] Dolgov A. A., “Turniry i gipoteza vershinnoi rekonstruiruemosti”, Nauka i obrazovanie: problemy i perspektivy, Materialy 9-i regionalnoi nauchno-prakticheskoi konferentsii aspirantov, studentov i uchaschikhsya (Biisk, 13–14 aprelya 2007 g.), 2007, 171–176