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

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2016},
     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
PB  - mathdoc
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
%I mathdoc
%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/