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This article is cited in 1 scientific paper (total in 1 paper)
Mathematics
On the number of $OE$-trails for a fixed transition system
T. A. Makarovskikh South Ural State University, Chelyabinsk, Russia
Abstract:
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.
Received: 29.06.2015
Citation:
T. A. Makarovskikh, “On the number of $OE$-trails for a fixed transition system”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 8:1 (2016), 5–12
Linking options:
https://www.mathnet.ru/eng/vyurm282 https://www.mathnet.ru/eng/vyurm/v8/i1/p5
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Abstract page: | 136 | Full-text PDF : | 186 | References: | 51 | First page: | 8 |
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