English

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 γr2(G)2γr(G)\gamma_{r2}(G)\leq 2\gamma_r(G) for every graph GG, where γr2(G)\gamma_{r2}(G) and γr(G)\gamma_r(G) denote the 22-rainbow domination number and the weak Roman domination number of GG, respectively. We characterize the extremal graphs for this inequality that are {K4,K4e}\{ K_4,K_4-e\}-free, and show that the recognition of the K5K_5-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}
}
R2 v1 2026-06-22T10:13:46.838Z