Weak edge-degree domination in hypergraphs
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 99-108 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we extend the notion of weak degree domination in graphs to hypergraphs and find relationships among the domination number, the weak edge-degree domination number, the independent domination number and the independence number of a given hypergraph.
In this paper we extend the notion of weak degree domination in graphs to hypergraphs and find relationships among the domination number, the weak edge-degree domination number, the independent domination number and the independence number of a given hypergraph.
Classification : 05C65, 05C69
Keywords: hypergraph; weak degree domination number; independent domination number; graph theory
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Acharya, Belmannu Devadas; Gupta, Purnima. Weak edge-degree domination in hypergraphs. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 99-108. http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a7/

[1] B. D.  Acharya: Contributions to the theories of hypergraphs, graphoids and graphs. PhD.  Thesis, Indian Institute of Technology, Bombay, 1975.

[2] B. D.  Acharya: Separability and acyclicity in hypergraphs. In: Proceedings of the Symposium on Graph Theory. ISI Lecture Notes in Mathematics, No. 4 (A. R.  Rao, ed.), The Macmillan Comp., Calcutta, 1979, pp. 65–83. | MR | Zbl

[3] B. D.  Acharya: On the cyclomatic number of a hypergraph. Discrete Mathematics 27 (1979), 111–116. | DOI | MR | Zbl

[4] B. D.  Acharya, M.  Las Vergnas: Hypergraphs with cyclomatic number zero, triangulated graphs and an inequality. J.  Combinatorial Theory, Ser.  B 33 (1982), 52–56. | DOI | MR

[5] B. D.  Acharya: Full sets in hypergraphs. Sankhya: The Indian J.  Statistics. Special Vol. 54 (1992), 1–6. | MR | Zbl

[6] B. D.  Acharya: Strongly Helly hypergraphs. J.  Ramanujan Math. Soc. 11 (1996), 139–144. | MR | Zbl

[7] B. D.  Acharya, Purnima Gupta: A direct inductive proof of a conjecture due to E.  Sampathkumar and L.  Pushpa Latha. Nat. Acad. Sci.-Letters 21 (1998), 84–90. | MR

[8] C.  Berge: Graphs and Hypergraphs. North-Holland Elsevier Publ., Amsterdam, 1973. | MR | Zbl

[9] C.  Berge: Hypergraphs. North-Holland Elsevier Publ., Amsterdam, 1989. | MR | Zbl

[10] F.  Dacar: Cyclicity in hypergraphs. Discrete Mathematics 182 (1998), 53–67. | DOI | MR

[11] A.  Gyarfas, M. S.  Jacobson, A. E.  Kezdy, and J.  Lehel: Odd cycles and $\theta $-cycles in hypergraphs. “Paul Erdös and his Mathematics: Research Communications”, Janos Bolyayi Mathematical Society, Budapest, 1990, pp. 96–98. | MR

[12] J. H.  Hattingh, R. C.  Laskar: On weak domination in graphs. Ars Comb. 49 (1998), 205–216. | MR

[13] T. W.  Haynes, S. T.  Hedetniemi, and P. J.  Slater: Fundamentals of Domination in Graphs. Marcel Dekker, New York, 1998. | MR

[14] M.  Lewin: On hypergraphs without significant cycles. J.  Combinatorial Theory, Ser.  B 20 (1976), 80–83. | DOI | MR | Zbl

[15] D.  Rautenbach: Bounds on the weak domination number. Australas. J. Comb. 18 (1998), 245–251. | MR | Zbl

[16] E.  Sampathkumar, L.  Pushpa Latha: Strong weak domination and domination balance in a graph. Discrete Mathematics 161 (1996), 235–242. | DOI | MR

[17] D. B.  West: Introduction to Graph Theory. Prentice Hall, New Jersey, 1996. | MR | Zbl