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2003 Nonexistence of a Weakly Neighbourly Polyhedral Map of Type {6, 6}
Nandini Nilakantan
Experiment. Math. 12(3): 257-262 (2003).

Abstract

For the existence of an n-vertex polyhedral map of type {p, p}, it is known that n must be {\small $\geq (p-1)^2$} and equality holds if and only if K is weakly neighbourly. In 2002, Brehm et al. saw that there is a unique polyhedral map of type {\small $\{5, 5\}$} on 16 vertices. In 1990, Brehm constructed a polyhedral map of type {\small $\{6, 6\}$} with 26 vertices. In this article, we prove that there do not exist any polyhedral maps of type {\small $\{6, 6\}$} on 25 vertices. As a consequence, we show that the minimum number of edges in polyhedral maps of Euler characteristic -25 is {\small $>$} 75.

Citation

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Nandini Nilakantan. "Nonexistence of a Weakly Neighbourly Polyhedral Map of Type {6, 6}." Experiment. Math. 12 (3) 257 - 262, 2003.

Information

Published: 2003
First available in Project Euclid: 15 June 2004

zbMATH: 1080.52506
MathSciNet: MR2034390

Subjects:
Primary: 51M20, 52B70, 57M20

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 3 • 2003
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