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Graphs and Combinatorics

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

Weighted Domination of Independent Sets

  • Ron AharoniEmail author
  • Irina Gorelik
Original Paper
  • 31 Downloads

Abstract

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.

Keywords

Graph Independence Domination Chordal graphs Trees 

Notes

References

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsTechnionHaifaIsrael

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