Maximal Independent Sets in Planar Triangulations
Combinatorics
2024-10-30 v1 Discrete Mathematics
Abstract
We show that every planar triangulation on vertices has a maximal independent set of size at most . This affirms a conjecture by Botler, Fernandes and Guti\'errez [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 , but restricted to triangulations.
Keywords
Cite
@article{arxiv.2410.21808,
title = {Maximal Independent Sets in Planar Triangulations},
author = {P. Francis and Abraham M. Illickan and Lijo M. Jose and Deepak Rajendraprasad},
journal= {arXiv preprint arXiv:2410.21808},
year = {2024}
}