DMGT

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ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 20(2) (2000) 173-180
DOI: 10.7151/dmgt.1117

NOTE ON THE WEIGHT OF PATHS IN PLANE TRIANGULATIONS OF MINIMUM DEGREE 4 AND 5

Tomás Madaras

Department of Geometry and Algebra
P.J. Safárik University
Jesenná 5, 041 54 Košice, Slovak Republic
e-mail: madaras@duro.upjs.sk

Abstract

The weight of a path in a graph is defined to be the sum of degrees of its vertices in entire graph. It is proved that each plane triangulation of minimum degree 5 contains a path P5 on 5 vertices of weight at most 29, the bound being precise, and each plane triangulation of minimum degree 4 contains a path P4 on 4 vertices of weight at most 31.

Keywords: weight of path, plane graph, triangulation.

2000 Mathematics Subject Classification: 05C10, 05C38, 52B10.

References

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Received 14 April 1999
Revised 20 August 2000