Parameterized Problems on Coincidence Graphs

  • Sylvain Guillemot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


A (k,r)-tuple is a word of length r on an alphabet of size k. A graph is (k,r)-representable if we can assign a (k,r)-tuple to each vertex such that two vertices are connected iff the associated tuples agree on some component. We study the complexity of several graph problems on (k,r)-representable graphs, as a function of the parameters k,r; the problems under study are Maximum Independent Set, Minimum Dominating Set and Maximum Clique. In this framework, there are two classes of interest: the graphs representable with tuples of logarithmic length (i.e. graphs (k,r)-representable with r = O(k logn)), and the graphs representable with tuples of polynomial length (i.e. graphs (k,r)-representable with r = poly(n)). In both cases, we show that the problems are computationally hard, though we obtain stronger hardness results in the second case. Our hardness results also allow us to derive optimality results for Multidimensional Matching and Disjoint r -Subsets.


Vertex Cover Maximum Clique Parameterized Problem Hardness Result Hash Family 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sylvain Guillemot
    • 1
  1. 1.LIRMMMontpellier

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