Discussiones Mathematicae Graph Theory 16(2) (1996)
207-217
DOI: https://doi.org/10.7151/dmgt.1035
ON LIGHT SUBGRAPHS IN PLANE GRAPHS OF MINIMUM DEGREE FIVE
Stanislav Jendrol' Department of Geometry and Algebra, P.J. Safárik
University, Jesenná 5 |
Tomáš Madaras Department of Geometry and Algebra, P.J. Šafárik
University |
Abstract
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars K1,3 and K1,4 and a light 4-path P4. The results obtained for K1,3 and P4 are best possible.
Keywords: planar graph, light subgraph, star, triangulation.
1991 Mathematics Subject Classification: 05C75, 05C10, 52B10.
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