Combinatorica

, Volume 22, Issue 1, pp 47–70 | Cite as

Graph Orientations with Edge-connection and Parity Constraints

  • András Frank
  • Zoltán Király
Original Paper

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 \(\) 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.

AMS Subject Classification (2000) Classes:  05C75, 05C40 

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Copyright information

© János Bolyai Mathematical Society, 2002

Authors and Affiliations

  • András Frank
    • 1
  • Zoltán Király
    • 2
  1. 1.Department of Operations Research, Eötvös University; Pázmány Péter sétány 1/c, Budapest, Hungary, H-1117; and Traffic Lab, Ericsson Hungary; Laborc u. 1, Budapest, Hungary H-1037; E-mail: frank@cs.elte.huHU
  2. 2.Department of Computer Science, Eötvös University; Pázmány Péter sétány 1/c, Budapest, Hungary, H-1117; and Traffic Lab, Ericsson Hungary; Laborc u. 1, Budapest, Hungary H-1037; E-mail: kiraly@cs.elte.huHU

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