# 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

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## References

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• 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.
Flow Graph Reducibility
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SIAM J. Comput.
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This work characterize the set of flow graphs that can be analyzed in this way in terms of two very simple transformations on graphs and gives a necessary and sufficient condition for analyzability and applies it to “goto-less programs,” showing that they all meet the criterion.
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• Mathematics
JACM
• 1978
The problem of finding two disjoint paths, P~ from s~ to tt and P2 from s2 to t2, is considered and efficient algorithms are proposed for these problems.
On the Complexity of Timetable and Multicommodity Flow Problems
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SIAM J. Comput.
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A very primitive version of Gotlieb’s timetable problem is shown to be NP-complete, and therefore all the common timetable problems are NP-complete. A polynomial time algorithm, in case all teachers
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The theorem that a meeting function always exists if all teachers and classes have no time constraints is proved and the multi-commodity integral flow problem is shown to be NP-complete even if the number of commodities is two.
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This work shows how to prove the undecidability of a problem by efficiently reducing the membership problem for Tms that always halt to it and introduces the forbidden subgraph problem.
The two paths problem is polynomial
Given an undirected graph G = (V,E) and vertices \$s_1\$,\$t_1\$;\$s_2\$,\$t_2\$, the problem is to determine whether or not G admits two vertex disjoint paths \$P_1\$ and \$P_2\$, connecting \$s_1\$ with \$t_1\$