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arXiv · 2410.21808

Maximal Independent Sets in Planar Triangulations

P. Francis·Abraham M. Illickan·Lijo M. Jose·Deepak Rajendraprasad
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Abstract

We show that every planar triangulation on $n$ vertices has a maximal independent set of size at most $n/3$. This affirms a conjecture by Botler, Fernandes and Gutiérrez [Electron.\ J.\ Comb., 2024], which in turn would follow if an open question of Goddard and Henning [Appl.\ Math.\ Comput., 2020] which asks if every planar triangulation has three disjoint maximal independent sets were answered in the affirmative. Since a maximal independent set is a special type of dominating set (independent dominating set), this is a structural strengthening of a major result by Matheson and Tarjan [Eur.\ J.\ Comb., 1996] that every triangulated disc has a dominating set of size at most $n/3$, but restricted to triangulations.

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P. Francis, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad. 2024-10-29. Maximal Independent Sets in Planar Triangulations. https://arxiv.org/abs/2410.21808

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