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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2024 Volume 21, Issue 1, Pages 370–382 (Mi semr1691)

Discrete mathematics and mathematical cybernetics

Small length circuits in Eulerian orientations of graphs

A. L. Perezhogina, I. S. Bykovb, S. V. Avgustinovicha

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia

Abstract: In this paper we investigate estimates for number of 3-, 4- and 5-circuits in eulerian tournaments and 4-circuits in eulerian orientations of complete bipartite graphs and hypercubes. By using obtained relations, we prove uniqueness (up to isomorphism) of orientations, which reach maximum number of 4-circuits in all graph families mentioned above.

Keywords: Eulerian orientation of graph, circuit, tournament, complete bipartite graph, boolean cube.

UDC: 519.175

MSC: 05C20

Received December 12, 2023, published June 6, 2024

DOI: doi.org/10.33048/semi.2024.21.028



© Steklov Math. Inst. of RAS, 2025