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On 3-Connected Plane Graphs without Triangular Faces

✍ Scribed by J. Harant; S. Jendrol'; M. Tkác

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
151 KB
Volume
77
Category
Article
ISSN
0095-8956

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✦ Synopsis

We prove that each polyhedral triangular face free map G on a compact 2-dimensional manifold M with Euler characteristic /(M) contains a k-path, i.e., a path on k vertices, such that each vertex of this path has, in G, degree at most (5Â2) k if M is a sphere S 0 and at most (kÂ2)w(5+-49&24/(M))Â2x if M{S 0 or does not contain any k-path. We show that for even k this bound is best possible. Moreover, we show that for any graph other than a path no similar estimation exists.

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