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}
}
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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.
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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 $t_1$…