On a problem of J. Zaks concerning 5-valent 3-connected planar graphs
type: Item
instance of: scholarly article
title: On a problem of J. Zaks concerning 5-valent 3-connected planar graphs
zbMATH Open document ID: 0538.05032
DOI: 10.1016/0012-365X(84)90051-7
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The author presents an affirmative solution of the following Eberhard- type problem, posed by J. Zaks: Let \((p_ 5,p_ 6,...)\) be a finite sequence of nonnegative integers; does there exist a 5-valent 3-connected planar graph G such that it has exactly \(p_ k\) k-gons for all \(k\geq 5\), \(m_ i\) of its vertices meet exactly i triangles, \(i=4,5\), and \(m_ 4+2m_ 5=24+3\sum_{k\geq 5}(k-4)p_ k?\) Moreover, some interesting relationships among certain sets of r-valent s-connected graphs embeddable in an orientable surface of genus g (for suitable triples (r,s,g)) are established.
reviewed by: Jozef Širáň
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 3855141
zbMATH Keywords: planar graph
zbMATH Keywords: Eberhard-type problem
author: Stanislav Jendroľ
MaRDI profile type: Publication
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full work available at URL: 0012-365x(84)90051-7
OpenAlex ID: W2161194290
description: scientific article; zbMATH DE number 3855141