Two arc-disjoint paths in Eulerian digraphs

András Frank, Toshihide Ibaraki, Hiroshi Nagamochi

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1 Citation (Scopus)


Let G bean Eulerian digraph, and let {x1,x2}, {y1, y2} be two pairs of vertices in G. A directed path from a vertex s to a vertex t is called an st-path. An instance (G; {x1, x2}, {y1, y2}) is called feasible if there is a choice of h,i,j,k with {h,i} = {j,k} = {1,2} such that G has two arc-disjoint XhXi- and yjyk-paths. In this paper, we characterize the structure of minimal infeasible instances, based on which an O(m + n log n) time algorithm is presented to decide whether a given instance is feasible, where n and m are the number of vertices and arcs in the instance, respectively. If the instance is feasible, the corresponding two arc-disjoint paths can be computed in O(m(m + n log n)) time.

Original languageEnglish
Pages (from-to)557-589
Number of pages33
JournalSIAM Journal on Discrete Mathematics
Issue number4
Publication statusPublished - Nov 1998



  • Disjoint paths
  • Eulerian digraph
  • Minimum cut
  • Planar graph
  • Polynomial time algorithm

ASJC Scopus subject areas

  • Mathematics(all)

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