On packing shortest cycles in graphs

  • Authors:

  • Dieter Rautenbach;Friedrich Regen

  • Affiliations:

  • Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany;Institut für Mathematik, TU Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

We study the problems to find a maximum packing of shortest edge-disjoint cycles in a graph of given girth g (g-ESCP) and its vertex-disjoint analogue g-VSCP. In the case g=3, Caprara and Rizzi (2001) have shown that g-ESCP can be solved in polynomial time for graphs with maximum degree 4, but is APX-hard for graphs with maximum degree 5, while g-VSCP can be solved in polynomial time for graphs with maximum degree 3, but is APX-hard for graphs with maximum degree 4. For g@?{4,5}, we show that both problems allow polynomial time algorithms for instances with maximum degree 3, but are APX-hard for instances with maximum degree 4. For each g=6, both problems are APX-hard already for graphs with maximum degree 3.