On Vizing's conjecture

• Autorzy: Bostjan Bresar
• Języki publikacji: EN

Abstrakty

EN

A dominating set D for a graph G is a subset of V(G) such that any vertex in V(G)-D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product G ⃞ H Vizing's conjecture [10] states that γ(G ⃞ H) ≥ γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G) = γ(H) = 3.

Słowa kluczowe

EN

graph; Cartesian product; domination number

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 5-11

Daty

wydano

2001

otrzymano

1999-12-09

poprawiono

2001-01-22

Twórcy

autor

Bostjan Bresar

• University of Maribor, FK, Vrbanska 30, 2000 Maribor, Slovenia

Bibliografia

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• [6] B. Hartnell and D.F. Rall, Vizing's conjecture and the one-half argument, Discuss. Math. Graph Theory 15 (1995) 205-216, doi: 10.7151/dmgt.1018.
• [7] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs I, Ars Combin. 18 (1983) 33-44.
• [8] M.S. Jacobson and L.F. Kinch, On the domination number of products of graphs II: Trees, J. Graph Theory 10 (1986) 97-106, doi: 10.1002/jgt.3190100112.
• [9] S. Klavžar and N. Seifter, Dominating Cartesian product of cycles, Discrete Appl. Math. 59 (1995) 129-136, doi: 10.1016/0166-218X(93)E0167-W.
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Identyfikatory

DOI

10.7151/dmgt.1129