Geodesic
The Euler Tour of $n$-Dimensional Manifold with Positive Genus
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 110-113 
Cataranciuc Sergiu; Bujac-Leisz Mariana; Soltan Petru. The Euler Tour of $n$-Dimensional Manifold with Positive Genus. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 110-113. http://geodesic.mathdoc.fr/item/BASM_2008_2_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper [1] it is proved that abstract cubic $n$-dimensional torus [2] possesses a directed Euler tour of the same dimension. The result prompts to a new (virtual) device for transmission and reception of information. In the present paper it is shown that every abstract cubic $n$-dimensional manifold without borders, of positive genus possesses a $n$-dimensional directed Euler tour. This result has practical application.

[1] Bujac M., “The Application of Two-Dimensional Torus in the Transmission of Information”, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, vol. 4, Mediamira Science Publisher, Cluj-Napoca, 2006, 9–17

[2] Bujac M., “On the Multidimensional Directed Euler Tour of Cubic Manifold”, Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2006, no. 1(50), 15–22 | MR | Zbl

[3] Bujac M., Cataranciuc S., Soltan P., “On the Division of Abstract Manifolds in Cubes”, Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2006, no. 2(51), 29–34 | MR | Zbl

[4] Bujac M., Soltan P., “The Abstract Multidimensional Varieties and Their Classification”, Revue d'analyse numerique et de theorie de l'approximation, Cluj-Napoca, 33:2 (2004), 163–165 | MR | Zbl

[5] Soltan P., “On the Homologies on Multi-ary Relations and Oriented Hipergraphs”, Studii în metode de analiză numerică şi optimizare, Chişinău, 2:1(3) (2000) | MR

[6] Soltan P., Prisacaru C., “Zadacha Shteynera na grafakh”, DAN SSSR, 198:1 (1971) (in Russian) | MR | Zbl