Geodesic
On light subgraphs in plane graphs of minimum degree five
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 207-217

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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 P₄. The results obtained for K_1,3 and P₄ are best possible.
Keywords: planar graph, light subgraph, star, triangulation 
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Jendrol', Stanislav; Madaras, Tomáš. On light subgraphs in plane graphs of minimum degree five. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 207-217. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a10/