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How to induce a minimal subgraph

  1. Apr 6, 2012 #1
    I have a undirected graph G and a subset S of nodes from G. If I only do vertex-induced subgraph for S, this subgraph might not be connected. What I want to do is to include as few as possible extra nodes outside S, and make as most as possible nodes in S are connected pairwisely through a path. Is there any way to accomplish this?

    Thank you very much
     
  2. jcsd
  3. Apr 7, 2012 #2

    Stephen Tashi

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    Science Advisor

    I'm not a graph theorist, but I think you should clarify what it means to accomplish your goal. Are you asking whether there is an algorithm to construct the required subgraph? - or are you asking whether there is a theoretical argrument that the required subgraph exists?
     
  4. Apr 8, 2012 #3
    I would like to know whether such subgraph exists or not. If it does exist, is there an algorithm to obtain this subgraph
     
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