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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Finding a Maximum Induced Degenerate Subgraph Faster Than 2 n
verfasst von : Marcin Pilipczuk, Michał Pilipczuk
Erschienen in: Parameterized and Exact Computation
Verlag: Springer Berlin Heidelberg
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In this paper we study the problem of finding a maximum induced
d
-degenerate subgraph in a given
n
-vertex graph from the point of view of exact algorithms. We show that for any fixed
d
one can find a maximum induced
d
-degenerate subgraph in randomized
$(2-\varepsilon _d)^nn^{\mathcal{O}(1)}$
time, for some constant
ε
d
> 0 depending only on
d
. Moreover, our algorithm can be used to sample inclusion-wise maximal induced
d
-degenerate subgraphs in such a manner that every such subgraph is output with probability at least (2 −
ε
d
)
−
n
; hence, we prove that their number is bounded by (2 −
ε
d
)
n
.