Geodesic
On the number of $OE$-trails for a fixed transition system
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 8 (2016) no. 1, pp. 5-12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The existence of $OE$-trail for a plane Eulerian graph had been established earlier and algorithm of its constructing was suggested. This paper is devoted to a question of enumeration of $OE$-trails for a system of transitions induced by a particular $OE$-trail. The upper bound of this estimation does not exceed the double sum of vertices adjacent the outer face and sum of cutvertices degrees. This bound is reachable if a transition system satisfies any $A$-trail. The number of $OE$-trails for an arbitrary chosen transition system is also examined.
Keywords: planar graph; Eulerian cycle; transition system; $A$-trail; ordered enclosing. 
@article{VYURM_2016_8_1_a0,
     author = {T. A. Makarovskikh},
     title = {On the number of $OE$-trails for a fixed transition system},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {5--12},
     year = {2016},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2016_8_1_a0/}
}
TY  - JOUR
AU  - T. A. Makarovskikh
TI  - On the number of $OE$-trails for a fixed transition system
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2016
SP  - 5
EP  - 12
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VYURM_2016_8_1_a0/
LA  - ru
ID  - VYURM_2016_8_1_a0
ER  - 
%0 Journal Article
%A T. A. Makarovskikh
%T On the number of $OE$-trails for a fixed transition system
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2016
%P 5-12
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/VYURM_2016_8_1_a0/
%G ru
%F VYURM_2016_8_1_a0
T. A. Makarovskikh. On the number of $OE$-trails for a fixed transition system. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 8 (2016) no. 1, pp. 5-12. http://geodesic.mathdoc.fr/item/VYURM_2016_8_1_a0/

[1] Panyukova T. A., Diskretnyy analiz i issledovanie operatsiy, 18:2 (2011), 64–74 (in Russ.) | MR | Zbl

[2] T. A. Makarovskikh, “The Algorithm for Constructing of Cutter Optimal Path”, Journal of Computational and Engineering Mathematics, 1:2 (2014), 52–61

[3] Frolovskiy V. D., Informatsionnye tekhnologii v proektirovanii i proizvodstve, 2005, no. 4, 63–66 (in Russ.)

[4] T. A. Panioukova, A. V. Panyukov, “The Algorithm for Tracing of Flat Euler Cycles with Ordered Enclosing”, Izvestiya Chelyabinskogo nauchnogo tsentra UrO RAN, 2000, no. 4(9), 18–22 | MR

[5] H. Fleischner, Eulerian Graphs and Related Topics, v. 1, Ann. Discrete Mathematics, 45, 1990, 450 pp. | MR | Zbl

[6] Belyy S. B., Matematicheskie zametki, 34:4 (1983), 625–628 (in Russ.) | MR | Zbl

[7] Panyukova T. A., Diskretnyy analiz i issledovanie operatsiy. Ser. 2, 13:2 (2006), 31–43 (in Russ.) | MR | Zbl

[8] Panyukova T. A., “Construction of Euler cycles ordered grapple as a mathematical model of solving the cutting problem”, Modern information technology and IT education, Proceedings of the VIII International Scientific and Practical Conference, ed. V. A. Sukhomlin, INTUIT. RU Publ., M., 2013, 706–713 (in Russ.) | Zbl