This article is cited in 2 papers

Research articles

The Multidimensional Directed Euler Tour of Cubic Manifold

Mariana Bujac

Moldova State University, Chisinau, Moldova

Abstract: In the paper [3] we tried to generalize the problem of existence of a directed $(n-1)$-dimensional Euler tour for the abstract directed $n$-dimensional manifold, which is a complex of multi-ary relations [5], namely by means of abstract simplexes. In the paper [3] we show the existence of such kind of tour only for manifolds of odd dimension because we have not enough conditions to do more. In the present paper we will show conditions of existence for a directed Euler tour of abstract manifolds with even dimensions. In this purpose, we will introduce some new definitions which permit us to define manifolds by so-called abstract cubes.

Keywords and phrases: Abstract directed manifold, vacuum, Euler tour, abstract cube, abstract cubic complex, abstract cubic manifold, totally coherent manifold.

MSC: 18F15, 32Q60, 32C10

Received: 19.01.2006

Language: English

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