Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Abrosimov M. B., Dolgov A. A. About Reconstruction of Small Tournaments. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 2, pp. 94-98. DOI: 10.18500/1816-9791-2009-9-2-94-98

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
18.06.2009
Full text:
(downloads: 152)
Language: 
Russian
Heading: 
UDC: 
519.17

About Reconstruction of Small Tournaments

Autors: 
Abrosimov Mikhail Borisovich, Saratov State University
Dolgov Aleksandr Alekseevich, Saratov State University
Abstract: 

A tournament of order n is 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.

References: 
  1. Богомолов А.М., Салий В.Н. Алгебраические основы теории дискретных систем. М.: Наука, 1997.
  2. Харари Ф. Теория графов. М.: УРСС, 2003.
  3. Stockmeyer P. My quest for non-reconstructable graphs // Congressus Numerantium. 1988. V. 63. P. 188– 200.
  4. Долгов А.А. Турниры и гипотеза вершинной реконструируемости // Наука и образование: проблемы и перспективы: Материалы 9-й региональной научнопрактической конференции аспирантов, студентов и учащихся (Бийск, 13–14 апреля 2007г.). 2007. С. 171– 176.