## 19 Citations

### Detecting Fixed Patterns in Chordal Graphs in Polynomial Time

- MathematicsAlgorithmica
- 2013

The Contractibility problem takes as input two graphs G and H, and the task is to decide whether H can be obtained from G by a sequence of edge contractions, which is known to be NP-complete when k=2, and can be solved in polynomial time on chordal graphs even when k is part of the input.

### Polynomial-time algorithms for Subgraph Isomorphism in small graph classes of perfect graphsI

- Mathematics, Computer Science
- 2019

It is shown that even if the base graphs are somewhat restricted perfect graphs, the problem of finding a pattern graph that is a chain graph, a co-chain graph, or a threshold graph is NP-complete.

### Polynomial-time algorithms for Subgraph Isomorphism in small graph classes of perfect graphs

- MathematicsDiscret. Appl. Math.
- 2016

### Polynomial-Time Algorithms for Subgraph Isomorphism in Small Graph Classes of Perfect Graphs

- Mathematics, Computer Science
- 2014

### Contracting chordal graphs and bipartite graphs to paths and trees

- MathematicsDiscret. Appl. Math.
- 2011

### A note on contracting claw-free graphs

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2013

This work considers the problems that are to test whether a given host graph contains a fixed target graph as a contraction, and shows that these problems may become computationally easier when the host graphs are restricted to be claw-free.

### Contracting a Chordal Graph to a Split Graph or a Tree

- MathematicsMFCS
- 2011

It is shown that containment relations extending SUBGRAPH ISOMORPHISM can be solved in linear time if G is a chordal input graph and H is an arbitrary graph not part of the input.

### Induced Subtrees in Interval Graphs

- MathematicsIWOCA
- 2013

It is shown that the closely related Subtree Isomorphism problem is NP-complete even when G is restricted to the class of proper interval graphs, a well-known subclass of interval graphs.

### Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs

- MathematicsTheor. Comput. Sci.
- 2015

## References

SHOWING 1-10 OF 30 REFERENCES

### On Contracting Graphs to Fixed Pattern Graphs

- MathematicsSOFSEM
- 2010

The (H,v)-Contractibility problem, where v is a vertex of H, is studied and it is shown that this problem is NP-complete whenever H is connected and v is not a dominating graph of H.

### Induced Subgraph Isomorphism on Interval and Proper Interval Graphs

- MathematicsISAAC
- 2010

It is shown that when G is an interval graph and H is a connected proper interval graph, the problem is solvable in polynomial time and fixed parameter tractable when parametrised by the number of connected components of H.

### Contracting a Chordal Graph to a Split Graph or a Tree

- MathematicsMFCS
- 2011

It is shown that containment relations extending SUBGRAPH ISOMORPHISM can be solved in linear time if G is a chordal input graph and H is an arbitrary graph not part of the input.

### The computational complexity of graph contractions I: Polynomially solvable and NP‐complete cases

- MathematicsNetworks
- 2008

Interestingly, in all connected cases that are known to be polynomially solvable, the pattern graph H has a dominating vertex, whereas in all cases that isknown to be NP-complete, thepattern graph H does not have a dominating vertices.

### The computational complexity of graph contractions II: Two tough polynomially solvable cases

- MathematicsNetworks
- 2008

Here, polynomial time algorithms for these two remaining pattern graphs are presented, Interestingly, in all connected cases that are known to be polynomially solvable, the pattern graph H has a dominating vertex, whereas in all cases that isknown to be NP-complete, thepattern graph H does not have a dominating vertices.

### Contractions of Planar Graphs in Polynomial Time

- MathematicsESA
- 2010

It is proved that for every graph H, there exists a polynomial-time algorithm deciding if a planar graph can be contracted to H, and how to reduce finding embedded topological minors in plane graphs to solving an instance of the disjoint paths problem is shown.

### On the complexity of finding iso- and other morphisms for partial k-trees

- MathematicsDiscret. Math.
- 1992

### Contractibility and NP-completeness

- MathematicsJ. Graph Theory
- 1987

The complexity of H-CON is studied for H belonging to certain classes of graphs, together covering all connected graphs of order at most 4, which is NP-complete if H is a connected triangle-free graph other than a star.