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A finiteness theorem for maximal independent sets

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Abstract

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG ≅ K 1) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| ≤ 2k−1 +k − 2 for anyG inS(k) andk ≥ 2; consequently,S(k) is finite for anyk.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, 30050, Hsinchu, Taiwan

    Min-Jen Jou & Gerard J. Chang

  2. Department of Mathematics, National Central University, 32054, Chungli, Taiwan

    Chiang Lin

  3. Institute of Information Science, Academia Sinica, 11529, Nankang, Taipei, Taiwan

    Tze-Heng Ma

Authors
  1. Min-Jen Jou
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  2. Gerard J. Chang
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  3. Chiang Lin
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  4. Tze-Heng Ma
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Supported in part by the National Science Council under grant NSC 83-0208-M009-050

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Jou, MJ., Chang, G.J., Lin, C. et al. A finiteness theorem for maximal independent sets. Graphs and Combinatorics 12, 321–326 (1996). https://doi.org/10.1007/BF01858464

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  • DOI: https://doi.org/10.1007/BF01858464

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