On Light Edges and Triangles in Planar Graphs of Minimum Degree Five
Oleg Veniaminovich Borodin, Daniel P. Sanders · Mathematische Nachrichten · 1994
Abstract This paper presents two tight inequalities for planar graphs of minimum degree five. An edge or face of a plane graph is light if the sum of the degrees of the vertices incident with it is small. A light edge inequality is presented which shows that planar graphs of minimum degree five have a large number of light edges; a graph is presented which shows that this inequality cannot be improved. This completes work contributed to by Wernicke, Grünbaum, Fisk, and Borodin. A graph is presented which shows that a similar light triangle inequality of Borodin is best possible; no such graph had been previously found.