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∗

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

TLDR
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

Subgraph isomorphism in graph classes

Containment relations in split graphs

Edge contractions in subclasses of chordal graphs

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

The Longest Path Problem has a Polynomial Solution on Interval Graphs

TLDR
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.

Complement reducible graphs

Hamiltonian circuits in chordal bipartite graphs

An Optimal Greedy Heuristic to Color Interval Graphs

An improved algorithm for the longest induced path problem on k-chordal graphs