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## Discussiones Mathematicae Graph Theory

2002 | 22 | 1 | 199-210
Tytuł artykułu

### Domination in partitioned graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let V₁, V₂ be a partition of the vertex set in a graph G, and let $γ_i$ denote the least number of vertices needed in G to dominate $V_i$. We prove that γ₁+γ₂ ≤ [4/5]|V(G)| for any graph without isolated vertices or edges, and that equality occurs precisely if G consists of disjoint 5-paths and edges between their centers. We also give upper and lower bounds on γ₁+γ₂ for graphs with minimum valency δ, and conjecture that γ₁+γ₂ ≤ [4/(δ+3)]|V(G)| for δ ≤ 5. As δ gets large, however, the largest possible value of (γ₁+γ₂)/|V(G)| is shown to grow with the order of (logδ)/(δ).
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
199-210
Opis fizyczny
Daty
wydano
2002
otrzymano
2000-11-10
poprawiono
2001-05-09
Twórcy
autor
• Computer and Automation Institute, Hungarian Academy of Sciences, Budapest
• Department of Computer Science, University of Veszprém, Hungary
• Department of Mathematics, Aalborg University, Fredrik Bajers Vej 7E, DK-9220, Aalborg Ø, Denmark
Bibliografia
• [1] B.L. Hartnell and P.D. Vestergaard, Partitions and dominations in a graph, Manuscript, pp. 1-10.
• [2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs (Marcel Dekker, Inc., New York, N.Y., 1998).
• [3] C. Payan and N.H. Xuong, Domination-balanced graphs, J. Graph Theory 6 (1982) 23-32, doi: 10.1002/jgt.3190060104.
• [4] B. Reed, Paths, stars and the number three, Combin. Probab. Comput. 5 (3) (1996) 277-295, doi: 10.1017/S0963548300002042.
• [5] S.M. Seager, Partition dominations of graphs of minimum degree 2, Congressus Numerantium 132 (1998) 85-91.
Typ dokumentu
Bibliografia
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