@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… Expand

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… Expand

2015 IEEE International Conference on Big Data (Big Data)

2015

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.Expand

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.Expand