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Packing Euler graphs with traces

In: Operations Research Proceedings 2011

Author

Listed:
  • Peter Recht

    (Operations Research undWirtschaftsinformatik, TU Dortmund)

  • Eva-Maria Sprengel

    (Operations Research undWirtschaftsinformatik, TU Dortmund)

Abstract

For a graph G = (V,E) and a vertex v ∈ V, let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walkW(v), with start vertex v can be extended to an Eulerian tour in T(v). In general, local traces are not unique. We prove that if G is Eulerian every maximum edge-disjoint cycle packing Z* of G induces maximum local traces T(v) at v for every v ∈ V. In the opposite, if the total size $$ \sum $$V∈E|(T(v)|| is minimal then the set of related edge-disjoint cycles in G must be maximum.

Suggested Citation

  • Peter Recht & Eva-Maria Sprengel, 2012. "Packing Euler graphs with traces," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 53-58, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_9
    DOI: 10.1007/978-3-642-29210-1_9
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