# Induced Subtrees in Interval Graphs

@inproceedings{Heggernes2013InducedSI, title={Induced Subtrees in Interval Graphs}, author={Pinar Heggernes and Pim van 't Hof and Martin Milani{\vc}}, booktitle={IWOCA}, year={2013} }

The Induced Subtree Isomorphism problem takes as input a graph G and a tree T, and the task is to decide whether G has an induced subgraph that is isomorphic to T. This problem is known to be NP-complete on bipartite graphs, but it can be solved in polynomial time when G is a forest. We show that Induced Subtree Isomorphism can be solved in polynomial time when G is an interval graph. In contrast to this positive result, we show that the closely related Subtree Isomorphism problem is NP…

## 2 Citations

### Finding an Induced Subtree in an Intersection Graph is often hard∗

- Mathematics
- 2012

We prove that the induced subtree isomorphism problem is NP-complete for penny graphs and chordal graphs as text graphs. As a step in the proofs, we reprove that the problem is NPcomplete if the text…

### Identifying smallest unique subgraphs in a heterogeneous social network

- Mathematics2015 IEEE International Conference on Big Data (Big Data)
- 2015

An Ego-Graph Heuristic (EGH) method is developed to efficiently solve the SUS problem in an approximated manner and it is proved SUS is a NP-complete problem through doing a reduction from Minimum Vertex Cover in a homogeneous tree structure.

## References

SHOWING 1-10 OF 29 REFERENCES

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

- MathematicsTheor. Comput. Sci.
- 2015

### Edge contractions in subclasses of chordal graphs

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

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

- MathematicsDiscret. Math.
- 1992

### The Longest Path Problem has a Polynomial Solution on Interval Graphs

- Mathematics, Computer ScienceAlgorithmica
- 2010

The longest path problem can be solved in polynomial time on interval graphs with a dynamic programming approach and runs in O(n4) time, where n is the number of vertices of the input graph.

### A Simple Polynomial Algorithm for the Longest Path Problem on Cocomparability Graphs

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2012

This paper provides the first polynomial algorithm for the longest path problem on a much greater class, namely on cocomparability graphs, and uses a similar, but essentially simple algorithm.

### Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph

- MathematicsSIAM J. Comput.
- 1972

This paper presents ways for constructing efficient algorithms for finding a minimum coloring, a minimum covering by cliques, a maximum clique, and a maximum independent set given a chordal graph.