On light subgraphs in plane graphs of minimum degree five
Stanislav Jendrol′, Tomáš Madaras · Discussiones Mathematicae Graph Theory · 1996
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.