Independent sets near the lower bound in bounded degree graphs

  title={Independent sets near the lower bound in bounded degree graphs},
  author={Zdeněk Dvoř{\'a}k and Bernard Lidick{\'y}},
By Brook's Theorem, every n-vertex graph of maximum degree at most Delta >= 3 and clique number at most Delta is Delta-colorable, and thus it has an independent set of size at least n/Delta. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an independent set of size at least n/Delta+k has a kernel of size O(k). 

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Maximum independent sets near the upper bound


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