Graph orientations with edge-connection and parity constraints

András Frank, Zoltán Király

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Parity (matching theory) and connectivity (network flows) are two main branches of combinatorial optimization. In an attempt to understand better their interrelation, we study a problem where both parity and connectivity requirements are imposed. The main result is a characterization of undirected graphs G = (V, E) having a k-edge-connected T-odd orientation for every subset T ⊆ V with |E| + |T| even. (T-odd orientation: the in-degree of v is odd precisely if v is in T.) As a corollary, we obtain that every (2k)-edge-connected graph with |V| + |E| even has a (k - 1)-edge-connected orientation in which the in-degree of every node is odd. Along the way, a structural characterization will be given for digraphs with a root-node s having k edge-disjoint paths from s to every node and k-1 edge-disjoint paths from every node to s.

Original languageEnglish
Pages (from-to)47-70
Number of pages24
JournalCombinatorica
Volume22
Issue number1
DOIs
Publication statusPublished - Dec 7 2002

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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