Geodesic
Small length circuits in Eulerian orientations of graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 370-382.

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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.
Mots-clés : Eulerian orientation of graph, circuit
Keywords: tournament, complete bipartite graph, boolean cube. 
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     author = {A. L. Perezhogin and I. S. Bykov and S. V. Avgustinovich},
     title = {Small length circuits in {Eulerian} orientations of graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {370--382},
     publisher = {mathdoc},
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     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a20/}
}
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A. L. Perezhogin; I. S. Bykov; S. V. Avgustinovich. Small length circuits in Eulerian orientations of graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 370-382. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a20/