Radoslav Fulek, Filip Morić, David Pritchard
Published 2010-06-12Version 1
The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method, we begin by proving the simpler related upper bounds (4(V-1)-E)/3 and 4V^2/3E on the diameter (for connected planar graphs), which are also tight.
Automorphism Groups of Planar Graphs
On existence of integral point sets and their diameter bounds
Gallai's path decomposition in planar graphs
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