A polyhedral graph is a 3-connected planar graph. We find the least possible order p(k,a) of a polyhedral graph containing a k-independent set of size a for all positive integers k and a. In the case k=1 and a even, we prove that the extremal graphs are exactly the vertex-face (radial) graphs of maximal planar graphs.
Independence numbers of polyhedral graphs
Maffucci R. W.
2024-01-01
Abstract
A polyhedral graph is a 3-connected planar graph. We find the least possible order p(k,a) of a polyhedral graph containing a k-independent set of size a for all positive integers k and a. In the case k=1 and a even, we prove that the extremal graphs are exactly the vertex-face (radial) graphs of maximal planar graphs.
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