# Highly connected counterexamples to a conjecture on α-domination

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 3, page 435-440
- ISSN: 2083-5892

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topZsolt Tuza. "Highly connected counterexamples to a conjecture on α-domination." Discussiones Mathematicae Graph Theory 25.3 (2005): 435-440. <http://eudml.org/doc/270229>.

@article{ZsoltTuza2005,

abstract = {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.},

author = {Zsolt Tuza},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; dominating set; α-domination},

language = {eng},

number = {3},

pages = {435-440},

title = {Highly connected counterexamples to a conjecture on α-domination},

url = {http://eudml.org/doc/270229},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Zsolt Tuza

TI - Highly connected counterexamples to a conjecture on α-domination

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 3

SP - 435

EP - 440

AB - 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.

LA - eng

KW - graph; dominating set; α-domination

UR - http://eudml.org/doc/270229

ER -

## References

top- [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. Zbl1068.05051
- [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.

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