Induced subgraph isomorphism for cographs is NP-complete
WG '90 Proceedings of the 16th international workshop on Graph-theoretic concepts in computer science
On the complexity of finding iso- and other morphisms for partial k-trees
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Linear-time certifying recognition algorithms and forbidden induced subgraphs
Nordic Journal of Computing
On Contracting Graphs to Fixed Pattern Graphs
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of 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
Contracting a chordal graph to a split graph or a tree
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Containment relations in split graphs
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
Contracting chordal graphs and bipartite graphs to paths and trees
Discrete Applied Mathematics
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Modifying a given graph to obtain another graph is a well-studied problem with applications in many fields. Given two input graphs G and H, the Contractibility problem is to decide whether H can be obtained from G by a sequence of edge contractions. This problem is known to be NP-complete already when both input graphs are trees of bounded diameter. We prove that Contractibility can be solved in polynomial time when G is a trivially perfect graph and H is a threshold graph, thereby giving the first classes of graphs of unbounded treewidth and unbounded degree on which the problem can be solved in polynomial time. We show that this polynomial-time result is in a sense tight, by proving that Contractibility is NP-complete when G and H are both trivially perfect graphs, and when G is a split graph and H is a threshold graph. If the graph H is fixed and only G is given as input, then the problem is called H-Contractibility. This problem is known to be NP-complete on general graphs already when H is a path on four vertices. We show that, for any fixed graph H, the H-Contractibility problem can be solved in polynomial time if the input graph G is a split graph.