2 research outputs found
Minor stars in plane graphs with minimum degree five
The weight of a subgraph in is the sum of the degrees in of
vertices of . The {\em height} of a subgraph in is the maximum
degree of vertices of in . A star in a given graph is minor if its
center has degree at most five in the given graph. Lebesgue (1940) gave an
approximate description of minor -stars in the class of normal plane maps
with minimum degree five. In this paper, we give two descriptions of minor
-stars in plane graphs with minimum degree five. By these descriptions, we
can extend several results and give some new results on the weight and height
for some special plane graphs with minimum degree five.Comment: 11 pages, 3 figure
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 and and a light 4-path Pâ‚„. The results obtained for and Pâ‚„ are best possible