A Local Property of Large Polyhedral Maps on Compact 2-Dimensional Manifolds |
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| Authors: | S Jendrol' H-J Voss |
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| Institution: | (1) Department of Geometry and Algebra, P.J. Šafárik University and Institute of Mathematics, Slovak Academy of Sciences, Jesenná 5, 041 54 Košice, Slovakia, XX;(2) Department of Algebra, Technical University Dresden, Mommsenstrasse 13, D-01062 Dresden, Germany, DE |
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| Abstract: | We prove that each polyhedral map G on a compact 2-manifold, which has large enough vertices, contains a k-path, a path on k vertices, such that each vertex of it has, in G, degree at most 6k; this bound being best possible for k even. Moreover, if G has large enough vertices of degree >6k, than it contains a k-path such that each its vertex has degree, in G, at most 5k; this bound is best possible for any k.
Received: December 8, 1997 Revised: April 27, 1998 |
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| Keywords: | and phrases path light graph compact 2-manifold embeddings of graphs |
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