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Independent dominating sets in planar triangulations
- Publication Year :
- 2023
-
Abstract
- In 1996, Matheson and Tarjan proved that every near planar triangulation on $n$ vertices contains a dominating set of size at most $n/3$, and conjectured that this upper bound can be reduced to $n/4$ for planar triangulations when $n$ is sufficiently large. In this paper, we consider the analogous problem for independent dominating sets: What is the minimum $\epsilon$ for which every near planar triangulation on $n$ vertices contains an independent dominating set of size at most $\epsilon n$? We prove that $2/7 \leq \epsilon \leq 5/12$. Moreover, this upper bound can be improved to $3/8$ for planar triangulations, and to $1/3$ for planar triangulations with minimum degree 5.<br />Comment: 9 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2308.02754
- Document Type :
- Working Paper