Geodesic
Highly connected counterexamples to a conjecture on α-domination
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 435-440.

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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.
Keywords: graph, dominating set, α-domination 
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Tuza, Zsolt. Highly connected counterexamples to a conjecture on α-domination. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 435-440. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a19/

[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.

[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.

[3] D.R. Woodall, Improper colourings of graphs, Pitman Res. Notes Math. Ser. 218 (1988) 45-63.