Relating $2$-rainbow domination to weak Roman domination
Combinatorics
2015-07-20 v1
Abstract
Addressing a problem posed by Chellali, Haynes, and Hedetniemi (Discrete Appl. Math. 178 (2014) 27-32) we prove for every graph , where and denote the -rainbow domination number and the weak Roman domination number of , respectively. We characterize the extremal graphs for this inequality that are -free, and show that the recognition of the -free extremal graphs is NP-hard.
Keywords
Cite
@article{arxiv.1507.04901,
title = {Relating $2$-rainbow domination to weak Roman domination},
author = {Jose D. Alvarado and Simone Dantas and Dieter Rautenbach},
journal= {arXiv preprint arXiv:1507.04901},
year = {2015}
}