34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
March 8-11, 2017
By Brook’s Theorem, every n-vertex graph of maximum degree at most ∆≥3 and clique number at most ∆ is ∆-colorable, and thus it has an independent set of size at least n/∆. 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/∆ +k has a kernel of size O(k).
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Zdeněk Dvořák and Bernard Lidický. "Independent Sets near the Lower Bound in Bounded Degree Graphs" Hannover, GermanyLeibniz International Proceedings in Informatics
(2017) p. 28
Available at: http://works.bepress.com/bernard-lidicky/33/