# The Directed Subgraph Homeomorphism Problem

```@article{Fortune1980TheDS,
title={The Directed Subgraph Homeomorphism Problem},
author={Steven Fortune and John E. Hopcroft and Jim Wyllie},
journal={Theor. Comput. Sci.},
year={1980},
volume={10},
pages={111-121}
}```
• Published 1 June 1978
• Mathematics
• Theor. Comput. Sci.
744 Citations
The subgraph homeomorphism problem on reducible flow graphs
• Mathematics
Graph Theory and Algorithms
• 1980
It is shown that for every fixed pattern graph, there is a polynomial-time algorithm to solve the subgraph homeomorphism problem if the input graphs are restricted to reducible flow graphs.
The subgraph homeomorphism problem
• Mathematics
STOC
• 1978
This work investigates the problem of finding a homeomorphic image of a “pattern” graph H in a larger input graph G and develops a linear time algorithm to determine if there exists a simple cycle containing three given nodes in G.
An approach to the k paths problem
It follows that under the same restriction, the subgraph homeomorphism problem is polynomial for any pattern graph with five or fewer edges if the input graph is k+2 -connected.
The Subgraph Homeomorphism Problem
• Mathematics
J. Comput. Syst. Sci.
• 1980
Finding a subdivision of a digraph
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Theor. Comput. Sci.
• 2015
Finding k Disjoint Paths in a Directed Planar Graph
It is shown that, for each fixed \$k\$, the problem of finding \$k\$ pairwise vertex-disjoint directed paths between given pairs of terminals in a directed planar graph is solvable in polynomial time.
Finding an induced subdivision of a digraph
• Mathematics
Electron. Notes Discret. Math.
• 2011
A Group Theoretical Approach to Disjoint Paths in Directed Graphs
This is in general a hard problem The problem is NP complete Knuth cf even if we restrict ourselves to planar undirected graphs Lynch assuming that k is variable On the other hand it is a deep result
Finding an induced subdivision of a digraph
• Mathematics
Theor. Comput. Sci.
• 2012