On packing shortest cycles in graphs

نویسندگان

  • Dieter Rautenbach
  • Friedrich Regen
چکیده

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.

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عنوان ژورنال:
  • Inf. Process. Lett.

دوره 109  شماره 

صفحات  -

تاریخ انتشار 2009