Engineering and Applied Science Letter
Vol. 3 (2020), Issue 3, pp. 10 – 14
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2020.0042
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2020.0042
A linear algorithm for minimum dominator colorings of orientations of paths
Michael Cary
Division of Resource Economics and Management, West Virginia University, Morgantown, WV, USA.; macary@mix.wvu.edu
Copyright ©2020 Michael Cary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: April 3, 2020 – Accepted: August 11, 2020 – Published: September 15, 2020
Abstract
In this paper we present an algorithm for finding a minimum dominator coloring of orientations of paths. To date this is the first algorithm for dominator colorings of digraphs in any capacity. We prove that the algorithm always provides a minimum dominator coloring of an oriented path and show that it runs in \(\mathcal{O}(n)\) time. The algorithm is available at https://github.com/cat-astrophic/MDC-orientations_of_paths/.
Keywords:
Dominator coloring, digraph, domination, algorithm.