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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

Izv. Saratov Univ. Math. Mech. Inform., 2009 Volume 9, Issue 2, Pages 94–98 (Mi isu51)

Computer science

About reconstruction of small tournaments

M. B. Abrosimov, A. A. Dolgov

Saratov State University, Chair of Theoretical Basis of Computer Security and Cryptography

Abstract: 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.

Key words: graph, tournament, reconstruction conjecture.

UDC: 519.17

DOI: 10.18500/1816-9791-2009-9-2-94-98



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