# 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} }

## 15 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.

### Parameterized Complexity of Induced Graph Matching on Claw-Free Graphs

- MathematicsAlgorithmica
- 2014

It is shown that Induced Graph Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph, and even admits a polynomial kernel when $$H$$H is a complete graph.

### 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).

## 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)|.

### Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs

- Mathematics, Computer ScienceSIAM J. Comput.
- 1996

A linear-time algorithm to recognize and represent proper circular-arc graphs and obtain a new proof of a characterization of proper interval graphs by forbidden subgraphs.

### The clique-separator graph for chordal graphs

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

### Subgraph isomorphism in planar graphs and related problems

- MathematicsSODA '95
- 1995

We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small…

### 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.