Independent sets near the lower bound in bounded degree graphs

@inproceedings{Dvok2017IndependentSN,
  title={Independent sets near the lower bound in bounded degree graphs},
  author={Zdeněk Dvoř{\'a}k and Bernard Lidick{\'y}},
  booktitle={STACS},
  year={2017}
}
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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