Some remarks on α-domination

• Autorzy: Franz Dahme , Dieter Rautenbach , Lutz Volkmann
• Języki publikacji: EN

Abstrakty

EN

Let α ∈ (0,1) and let $G = (V_G,E_G$) be a graph. According to Dunbar, Hoffman, Laskar and Markus [3] a set $D ⊆ V_G$ is called an α-dominating set of G, if $|N_G(u) ∩ D| ≥ αd_G(u)$ for all $u ∈ V_G∖D$. We prove a series of upper bounds on the α-domination number of a graph G defined as the minimum cardinality of an α-dominating set of G.

Słowa kluczowe

EN

α-domination; domination

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 3
• Strony: 423-430

Daty

wydano

2004

otrzymano

2003-03-31

poprawiono

2003-12-12

Twórcy

autor

Franz Dahme

• Lehrstuhl II für Mathematik, RWTH-Aachen, 52056 Aachen, Germany

autor

Dieter Rautenbach

• Forschungsinstitut für Diskrete Mathematik, Lennéstr. 2, D-53113 Bonn, Germany

autor

Lutz Volkmann

• Lehrstuhl II für Mathematik, RWTH-Aachen, 52056 Aachen, Germany

Bibliografia

• [1] N. Alon and J. Spencer, The probabilistic method, 2nd ed., (Wiley-Interscience Series in Discrete Math. and Optimization, 2000), doi: 10.1002/0471722154.
• [2] H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann. Math. Stat. 23(1952) 493-507, doi: 10.1214/aoms/1177729330.
• [3] 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.
• [4] J.F. Fink, M.S. Jacobson, L.F. Kinch and J. Roberts, On graphs having domination number half their order, Period. Math. Hungar. 16 (1985) 287-293, doi: 10.1007/BF01848079.
• [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, New York, 1998).
• [6] F. Dahme, D. Rautenbach and L. Volkmann, α-domination perfect trees, manuscript (2002).
• [7] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ., 38 (Amer. Math. Soc., Providence, RI, 1962).
• [8] C. Payan and N.H. Xuong, Domination-balanced graphs, J. Graph Theory 6 (1982) 23-32, doi: 10.1002/jgt.3190060104.
• [9] D.R. Woodall, Improper colourings of graphs, Pitman Res. Notes Math. Ser. 218 (1988) 45-63.

Identyfikatory

DOI

10.7151/dmgt.1241