On Edge-Independent Sets

  • Ton Kloks
  • Ching-Hao Liu
  • Sheung-Hung Poon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7924)

Abstract

A set of edges in a graph G is independent if no two elements are contained in a clique of G. The edge-independent set problem asks for the maximal cardinality of independent sets of edges. We show that the edge-clique graphs of cocktail parties have unbounded rankwidth. There is an elegant formula that solves the edge-independent set problem for graphs of rankwidth one, which are exactly distance-hereditary graphs, and related classes of graphs. We present a PTAS for the edge-independent set problem on planar graphs and show that the problem is polynomial for planar graphs without triangle separators. The set of edges of a bipartite graph is edge-independent. We show that the edge-independent set problem remains NP-complete for graphs in which every neighborhood is bipartite, i.e., the graphs without odd wheels.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ton Kloks
    • 1
  • Ching-Hao Liu
    • 1
  • Sheung-Hung Poon
    • 1
  1. 1.Department of Computer ScienceNational Tsing Hua UniversityTaiwan

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