# Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs

@article{Heggernes2015InducedSI, title={Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs}, author={Pinar Heggernes and Pim van 't Hof and Daniel Meister and Yngve Villanger}, journal={Theor. Comput. Sci.}, year={2015}, volume={562}, pages={252-269} }

## 16 Citations

### 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

### 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.

### On the complexity of various parameterizations of common induced subgraph isomorphism

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2014

### Combinatorics and Algorithms for Quasi-chain Graphs

- MathematicsIWOCA
- 2021

A decomposition theorem for quasi-chain graphs is proposed that implies an implicit representation for graphs in this class and efficient solutions for some algorithmic problems that are generally intractable.

### Critical properties of bipartite permutation graphs

- Mathematics
- 2020

The class of bipartite permutation graphs enjoys many nice and important properties. In particular, this class is critically important in the study of clique- and rank-width of graphs, because it is…

### Simultaneous Representation of Proper and Unit Interval Graphs

- MathematicsESA
- 2019

Simultaneous unit interval graphs can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G = (V, E) is the union of the simultaneous graphs.

### Algorithms and complexity for geodetic sets on planar and chordal graphs

- MathematicsISAAC
- 2020

The complexity of finding the geodetic number on subclasses of planar graphs and chordal graphs is studied and it is shown that \textsc{MGS} is NP-hard on interval graphs, thereby answering a question of Ekim et al. (LATIN, 2012).

### FO model checking of geometric graphs

- Computer Science, MathematicsIPEC
- 2017

This work studies the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs) and obtains new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs.

## References

SHOWING 1-10 OF 21 REFERENCES

### 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.

### Edge contractions in subclasses of chordal graphs

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2011

### Cleaning Interval Graphs

- MathematicsAlgorithmica
- 2011

The NP-hardness of the Induced Subgraph Isomorphism problem is shown, and fixed-parameter tractability of the problem with non-standard parameterization is proved, where the parameter is the difference |V(G)|−|V(H)|.

### The clique-separator graph for chordal graphs

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2009

### Random Separation: A New Method for Solving Fixed-Cardinality Optimization Problems

- MathematicsIWPEC
- 2006

A new randomized method, random separation, for solving fixed-cardinality optimization problems on graphs, i.e., problems concerning solutions with exactly a fixed number k of elements that optimize solution values is developed.

### Domination on Cocomparability Graphs

- MathematicsSIAM J. Discret. Math.
- 1993

The authors determine the algorithmic complexity of domination and variants on cocomparability graphs, a class of perfect graphs containing both the interval and the permutation graphs. Minimum…

### Simple Linear Time Recognition of Unit Interval Graphs

- Mathematics, Computer ScienceInf. Process. Lett.
- 1995