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On Edge-Independent Sets

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Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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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Author information

Authors and Affiliations

  1. Department of Computer Science, National Tsing Hua University, Taiwan

    Ton Kloks, Ching-Hao Liu & Sheung-Hung Poon

Authors
  1. Ton Kloks
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  2. Ching-Hao Liu
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  3. Sheung-Hung Poon
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Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, Charles Darwin University, 0909, Darwin, NT, Australia

    Michael Fellows

  2. School of High-Technology for Human Welfare, Tokai University, 317 Nishimo, 410-0395, Numazu, Japan

    Xuehou Tan

  3. Department of Computer Science, Montana State University, 59717, Bozeman, MT, USA

    Binhai Zhu

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Kloks, T., Liu, CH., Poon, SH. (2013). On Edge-Independent Sets. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_28

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  • DOI: https://doi.org/10.1007/978-3-642-38756-2_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38755-5

  • Online ISBN: 978-3-642-38756-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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