• Corpus ID: 232478913

Graph of uv-paths in 2-connected graphs

  title={Graph of uv-paths in 2-connected graphs},
  author={Eduardo Rivera Campo},
For a 2-connected graph G and vertices u, v of G we define an abstract graph P(Guv) whose vertices are the paths joining u and v in G, where paths S and T are adjacent if T is obtained from S by replacing a subpath Sxy of S with an internally disjoint subpath Txy of T . We prove that P(Guv) is always connected and give a necessary and a sufficient condition for connectedness in cases where the cycles formed by the replacing subpaths are restricted to a specific family of cycles of G. 

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