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On light subgraphs in plane graphs of minimum degree five. (English) Zbl 0877.05050
Summary: 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 $$K_{1,3}$$ and $$K_{1,4}$$ and a light 4-path $$P_4$$. The results obtained for $$K_{1,3}$$ and $$P_4$$ are best possible.

##### MSC:
 05C75 Structural characterization of families of graphs 05C10 Planar graphs; geometric and topological aspects of graph theory 52B10 Three-dimensional polytopes
##### Keywords:
triangulation; plane graph; subgraph; stars
Full Text:
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