Random procedures for dominating sets in bipartite graphs

• Autorzy: Sarah Artmann , Jochen Harant
• Języki publikacji: EN

Abstrakty

EN

Using multilinear functions and random procedures, new upper bounds on the domination number of a bipartite graph in terms of the cardinalities and the minimum degrees of the two colour classes are established.

Słowa kluczowe

EN

domination; bipartite graph; multilinear function; random procedure

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 2
• Strony: 277-288

Daty

wydano

2010

otrzymano

2008-11-12

poprawiono

2009-08-10

zaakceptowano

2009-11-09

Twórcy

autor

Sarah Artmann

• Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany

autor

Jochen Harant

• Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany

Bibliografia

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• [3] S. Artmann, F. Göring, J. Harant, D. Rautenbach and I. Schiermeyer, Random procedures for dominating sets in graphs, submitted.
• [4] Y. Caro, New results on the independence number (Technical Report. Tel-Aviv University, 1979).
• [5] Y. Caro and Y. Roditty, On the vertex-independence number and star decomposition of graphs, Ars Combin. 20 (1985) 167-180.
• [6] Y. Caro and Y. Roditty, A note on the k-domination number of a graph, Internat. J. Math. Sci. 13 (1990) 205-206, doi: 10.1155/S016117129000031X.
• [7] G.J. Chang and G.L. Nemhauser, The k-domination and k-stability problems in sun-free chordal graphs, SIAM J. Algebraic Discrete Methods 5 (1984) 332-345, doi: 10.1137/0605034.
• [8] F. Göring and J. Harant, On domination in graphs, Discuss. Math. Graph Theory 25 (2005) 7-12, doi: 10.7151/dmgt.1254.
• [9] J. Harant and A. Pruchnewski, A note on the domination number of a bipartite graph, Ann. Combin. 5 (2001) 175-178, doi: 10.1007/PL00001298.
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• [11] J. Harant and D. Rautenbach, Domination in bipartite graphs, Discrete Math. 309 (2009) 113-122, doi: 10.1016/j.disc.2007.12.051.
• [12] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, Inc., New York, 1998).
• [13] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs Advanced Topics (Marcel Dekker, Inc., New York, 1998).
• [14] C. Payan, Sur le nombre d'absorption d'un graphe simple, (French), Cah. Cent. Étud. Rech. Opér. 17 (1975) 307-317.
• [15] V.K. Wei, A lower bound on the stability number of a simple graph, Bell Laboratories Technical Memorandum 81-11217-9 (Murray Hill, NJ, 1981).

Identyfikatory

DOI

10.7151/dmgt.1494