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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
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