The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
Partitioning graphs into connected parts
Theoretical Computer Science
Contractions of planar graphs in polynomial time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Edge contractions in subclasses of chordal graphs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
The computational complexity of disconnected cut and 2K2-partition
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Parameterized complexity of finding small degree-constrained subgraphs
Journal of Discrete Algorithms
On graph contractions and induced minors
Discrete Applied Mathematics
Finding contractions and induced minors in chordal graphs via disjoint paths
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Parameterized Complexity
Obtaining planarity by contracting few edges
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Obtaining planarity by contracting few edges
Theoretical Computer Science
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
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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.