Nonexistence of weakly neighborly polyhedral maps on the orientable 2-manifold of genus 2

Amos Altshuler; Ulrich Brehm

doi:10.1016/0097-3165(86)90008-7

Nonexistence of weakly neighborly polyhedral maps on the orientable 2-manifold of genus 2

Amos Altshuler, Ulrich Brehm

Department of Mathematics

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Abstract

A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without boudary, such that for every two vertices there is a 2-cell containing them. We prove that there are no w.n.p. maps on the orientable 2-manifold of genus 2. Genus 2 seems to be unique with respect to this property.

Original language	English
Pages (from-to)	87-103
Number of pages	17
Journal	Journal of Combinatorial Theory - Series A
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(86)90008-7
State	Published - 1 Jan 1986

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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title = "Nonexistence of weakly neighborly polyhedral maps on the orientable 2-manifold of genus 2",

abstract = "A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without boudary, such that for every two vertices there is a 2-cell containing them. We prove that there are no w.n.p. maps on the orientable 2-manifold of genus 2. Genus 2 seems to be unique with respect to this property.",

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AB - A weakly neighborly polyhedral map (w.n.p. map) is a 2-dimensional cell-complex which decomposes a closed 2-manifold without boudary, such that for every two vertices there is a 2-cell containing them. We prove that there are no w.n.p. maps on the orientable 2-manifold of genus 2. Genus 2 seems to be unique with respect to this property.

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Nonexistence of weakly neighborly polyhedral maps on the orientable 2-manifold of genus 2

Abstract

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