Independence numbers of polyhedral graphs
S\'ebastien Gaspoz, Riccardo W. Maffucci

TL;DR
This paper determines the minimum size of polyhedral graphs that contain a specified independent set, revealing that for certain parameters, extremal graphs are exactly the vertex-face graphs of maximal planar graphs.
Contribution
It introduces the function p(k,a) for minimal order of polyhedral graphs with given independent set size and characterizes extremal graphs for specific cases.
Findings
Calculated p(k,a) for various k and a.
Identified extremal graphs as vertex-face graphs in specific cases.
Provided structural insights into polyhedral graphs with large independent sets.
Abstract
A polyhedral graph is a -connected planar graph. We find the least possible order of a polyhedral graph containing a -independent set of size for all positive integers and . In the case and even, we prove that the extremal graphs are exactly the vertex-face (radial) graphs of maximal planar graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Optimization and Search Problems
