In 1996, Matheson and Tarjan conjectured that any n-vertex triangulation with n sufficiently large has a dominating set of size at most n/4. We prove this for graphs of maximum degree 6.
@article{arxiv.0806.2421,
title = {Dominating Sets in Plane Triangulations},
author = {Erika L. C. King and Michael J. Pelsmajer},
journal= {arXiv preprint arXiv:0806.2421},
year = {2010}
}
Comments
14 pages, 6 figures; Revised lemmas 6-8, clarified arguments and fixed typos, result unchanged