Independence numbers of polyhedral graphs

Sébastien Gaspoz and Riccardo W. Maffucci

Applied Mathematics and Computation, 2024, vol. 462, issue C

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.

Keywords: Independent set; Extremal problem; Planar graph; 3-polytope; Radial graph (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005180

DOI: 10.1016/j.amc.2023.128349

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