Orientations and detachments of graphs with prescribed degrees and connectivity

Satoru Iwata, Tibor Jordán

Research output: Contribution to journalArticle

Abstract

We give a necessary and sufficient condition for a graph to have an orientation that has k edge-disjoint arborescences rooted at a designated vertex s subject to lower and upper bounds on the in-degree at each vertex. The result is used to derive a characterization of graphs having a detachment that contains k edge-disjoint spanning trees. Efficient algorithms for finding those orientations and detachments are also described. In particular, the paper provides an algorithm for finding a connected (loopless) detachment in O(nm) time, improving on the previous best running time bound, where n and m denote the numbers of vertices and edges, respectively.

Original languageEnglish
Pages (from-to)121-128
Number of pages8
JournalDiscrete Optimization
Volume12
Issue number1
DOIs
Publication statusPublished - May 2014

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Keywords

  • Arborescence
  • Detachment
  • Graph
  • Orientation
  • Spanning tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

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