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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2024, Volume 21, Issue 1, Pages 370–382
DOI: https://doi.org/doi.org/10.33048/semi.2024.21.028 (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
Full-text PDF (432 kB)
DOI: https://doi.org/doi.org/10.33048/semi.2024.21.028
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0018
Received December 12, 2023, published June 6, 2024
Document Type: Article
UDC: 519.175
MSC: 05C20
Language: Russian
Citation: A. L. Perezhogin, I. S. Bykov, S. V. Avgustinovich, “Small length circuits in Eulerian orientations of graphs”, Sib. Èlektron. Mat. Izv., 21:1 (2024), 370–382
Citation in format AMSBIB
\Bibitem{PerBykAvg24}
\by A.~L.~Perezhogin, I.~S.~Bykov, S.~V.~Avgustinovich
\paper Small length circuits in Eulerian orientations of graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2024
\vol 21
\issue 1
\pages 370--382
\mathnet{http://mi.mathnet.ru/semr1691}
\crossref{https://doi.org/doi.org/10.33048/semi.2024.21.028}
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