On light subgraphs in plane graphs of minimum degree five

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 ${\displaystyle K_{1,3}}$ and ${\displaystyle K_{1,4}}$ and a light 4-path P₄. The results obtained for ${\displaystyle K_{1,3}}$ and P₄ are best possible.