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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Increasing the Minimum Degree of a Graph by Contractions
verfasst von : Petr A. Golovach, Marcin Kamiński, Daniël Paulusma, Dimitrios M. Thilikos
Erschienen in: Parameterized and Exact Computation
Verlag: Springer Berlin Heidelberg
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The
Degree Contractibility
problem is to test whether a given graph
G
can be modified to a graph of minimum degree at least
d
by using at most
k
contractions. We prove the following three results. First,
Degree Contractibility
is
NP
-complete even when
d
= 14. Second, it is fixed-parameter tractable when parameterized by
k
and
d
. Third, it is
W
[1]-hard when parameterized by
k
. We also study its variant where the input graph is weighted, i.e., has some edge weighting and the contractions preserve these weights. The
Weighted Degree Contractibility
problem is to test if a weighted graph
G
can be contracted to a weighted graph of minimum weighted degree at least
d
by using at most
k
weighted contractions. We show that this problem is
NP
-complete and that it is fixed-parameter tractable when parameterized by
k
.