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arXiv · 1609.09134

Independent sets near the lower bound in bounded degree graphs

Zdenek Dvorak·Bernard Lidicky
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Abstract

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 indepdendent set of size at least n/Delta+k has a kernel of size O(k).

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Zdenek Dvorak, Bernard Lidicky. 2016-10-03. Independent sets near the lower bound in bounded degree graphs. https://doi.org/10.4230/lipics.stacs.2017.28

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