A local property of polyhedral maps on compact two-dimensional manifolds
type: Item
instance of: scholarly article
title: A local property of polyhedral maps on compact two-dimensional manifolds
zbMATH Open document ID: 0946.05029
DOI: 10.1016/S0012-365X(99)00329-5
published in: Discrete Mathematics
publication date: 2000-10-18T00:00:00Z
review text: The authors show that, for any \(k\), each polyhedral map \(G\) on a compact connected surface with Euler characteristic \(\chi\) either contains a path on \(k\) vertices such that each vertex on the path has degree at most \(k\lfloor (5+\sqrt{49-24\chi})/2\rfloor\), or it contains no path on \(k\) vertices at all. Remarkably, no analogous result holds for any connected subgraphs other than paths.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1420218
zbMATH Keywords: surface
zbMATH Keywords: polyhedral map
zbMATH Keywords: path
zbMATH Keywords: degree of a vertex
author: Stanislav Jendroľ
author: Heinz-Juergen Voss
reviewed by: Jozef Širáň
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00329-5
OpenAlex ID: W2084280347
description: scientific article; zbMATH DE number 1420218