An infinite class of counterexamples is given to a conjecture of Dahme et al. [1] concerning the minimum size of a dominating vertex set that contains at least a prescribed proportion of the neighbors of each vertex not belonging to the set.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1295,
author = {Zsolt Tuza},
title = {Highly connected counterexamples to a conjecture on $\alpha$-domination},
journal = {Discussiones Mathematicae Graph Theory},
volume = {25},
year = {2005},
pages = {435-440},
zbl = {1102.05044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1295}
}
Zsolt Tuza. Highly connected counterexamples to a conjecture on α-domination. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 435-440. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1295/
[000] [1] F. Dahme, D. Rautenbach and L. Volkmann, Some remarks on α-domination, Discuss. Math. Graph Theory 24 (2004) 423-430, doi: 10.7151/dmgt.1241. | Zbl 1068.05051
[001] [2] J.E. Dunbar, D.G, Hoffman, R.C. Laskar and L.R. Markus, α-domination, Discrete Math. 211 (2000) 11-26, doi: 10.1016/S0012-365X(99)00131-4.
[002] [3] D.R. Woodall, Improper colourings of graphs, Pitman Res. Notes Math. Ser. 218 (1988) 45-63.