Graphs and Combinatorics

, Volume 35, Issue 3, pp 719–727 | Cite as

Weighted Domination of Independent Sets

  • Ron AharoniEmail author
  • Irina Gorelik
Original Paper


The independent domination number\(\gamma ^i(G)\) of a graph G is the maximum, over all independent sets I, of the minimal number of vertices needed to dominate I. It is known (Aharoni et al. in Combinatorica 22:335–343, 2002) that in chordal graphs \(\gamma ^i\) is equal to \(\gamma \), the ordinary domination number. The weighted version of this result is not true, but we show that it does hold for interval graphs, and for the intersection graphs of subtrees of a given tree, where each subtree is a single edge.


Graph Independence Domination Chordal graphs Trees 



  1. 1.
    Aharoni, R., Berger, E., Ziv, R.: A tree version of König’s theorem. Combinatorica 22, 335–343 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aharoni, R., Haxell, P.: Hall’s theorem for hypergraphs. J. Combin. Theorey 35, 83–88 (2000)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Gavril, F.: The intersection graphs of subtrees in trees are exactly the chordal graphs. J. Combin. Theory Ser. B 16, 47–56 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Meshulam, R.: The clique complex and hypergraph matching. Combinatorica 21, 89–94 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Roberts, F.S.: Indifference graphs. In: Haray, F. (ed.) Proof Techniques in Graph Theory, pp. 139–146. Academic Press, New York (1969)Google Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsTechnionHaifaIsrael

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