The weakly neighborly polyhedral maps on the non-orientable 2-manifold with Euler characteristic -2
type: Item
instance of: scholarly article
title: The weakly neighborly polyhedral maps on the non-orientable 2-manifold with Euler characteristic -2
zbMATH Open document ID: 0623.51012
DOI: 10.1016/0097-3165(87)90048-3
author: Amos Altshuler
author: Ulrich Brehm
published in: Journal of Combinatorial Theory. Series A
publication date: 1987-01-01T00:00:00Z
review text: In this paper a classification is given of all weakly neighborly polyhedral maps on the Klein bottle with one handle, compare the general treatment by the authors in Isr. J. Math. 53, 137-157 (1986; Zbl 0592.51016). It is found that there are exactly 8 different maps of that kind, 6 with 9 vertices, 16 triangles and 3 quadrilaterals, 2 with 10 vertices, 15 triangles and 3 pentagons. The proof follows the pattern of the corresponding result for the orientable surface of genus two in which case such a map does not exist, see the authors in J. Comb. Theory, Ser. A 42, 87-103 (1986; Zbl 0585.57004).
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 4011336
zbMATH Keywords: weakly neighborly polyhedral maps on the Klein bottle with one handle
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: 0097-3165(87)90048-3
OpenAlex ID: W2005192773
cites work: Nonexistence of weakly neighborly polyhedral maps on the orientable 2- manifold of genus 2
cites work: The weakly neighborly polyhedral maps on the 2-manifold with Euler characteristic -1
cites work: On weakly neighborly polyhedral maps of arbitrary genus
cites work: The weakly neighborly polyhedral maps on the torus
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description: scientific article; zbMATH DE number 4011336