Near Polygons Having a big sub Near Polygon Isomorphic to

Bart De Bruyn

Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium

bdb@cage.rug.ac.be

Annals of Combinatorics 6 (3) p.285-294 September, 2002

Abstract:

In [1] a near 2n-gon
,,
was constructed from the set of 2-factors of the complete graph on 2n+2 vertices.
In this paper, we determine all near 2n-gons, ,
having as a big geodetically closed
sub near 2(n-1)-gon under the additional assumption that every two points at
distance 2 have at least two common neighbours. We will prove that such a near
2n-gon is either isomorphic to or
to a direct product of with a line.
As a corollary of that, the near polygon is
characterized by means of the local space at one point.

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