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Generalized Powers of Graphs and Their Algorithmic Use

  • Andreas Brandstädt
  • Feodor F. Dragan
  • Yang Xiang
  • Chenyu Yan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)

Abstract

Motivated by the frequency assignment problem in heterogeneous multihop radio networks, where different radio stations may have different transmission ranges, we introduce two new types of coloring of graphs, which generalize the well-known Distance-k-Coloring. Let G=(V,E) be a graph modeling a radio network, and assume that each vertex v of G has its own transmission radius r(v), a non-negative integer. We define r-coloring (r  +  -coloring) of G as an assignment Φ: V↦{0,1,2,...} of colors to vertices such that Φ(u)=Φ(v) implies d G (u,v)>r(v)+r(u) (d G (u,v)>r(v)+r(u)+1, respectively). The r-Coloring problem (the r  +  -Coloring problem) asks for a given graph G and a radius-function r: VN∪{0}, to find an r-coloring (an r  + -coloring, respectively) of G with minimum number of colors. Using a new notion of generalized powers of graphs, we investigate the complexity of the r-Coloring and r  + -Coloring problems on several families of graphs.

Keywords

Planar Graph Radio Station Interval Graph Chordal Graph Coloring Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  • Feodor F. Dragan
    • 2
  • Yang Xiang
    • 2
  • Chenyu Yan
    • 2
  1. 1.FB InformatikUniversität RostockRostockGermany
  2. 2.Department of Computer ScienceKent State UniversityKentUSA

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