## 744 Citations

The subgraph homeomorphism problem on reducible flow graphs

- MathematicsGraph 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

- MathematicsSTOC
- 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

- MathematicsSTOC '80
- 1980

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.

Finding k Disjoint Paths in a Directed Planar Graph

- MathematicsSIAM J. Comput.
- 1994

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

- MathematicsElectron. Notes Discret. Math.
- 2011

A Group Theoretical Approach to Disjoint Paths in Directed Graphs

- Mathematics
- 1993

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…

## References

SHOWING 1-7 OF 7 REFERENCES

The subgraph homeomorphism problem

- MathematicsSTOC
- 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

- Computer ScienceSIAM J. Comput.
- 1972

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.

Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph

- MathematicsJACM
- 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

- Computer ScienceSIAM J. Comput.
- 1976

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…

On the complexity of time table and multi-commodity flow problems

- Computer Science16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
- 1975

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.

Dichotomization, reachability, and the forbidden subgraph problem(Extended Abstract)

- Computer Science, MathematicsSTOC '76
- 1976

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

- Mathematics
- 1978

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 $t_1$…