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On packing shortest cycles in graphs. (English) Zbl 1197.05119
Summary: 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 $$g=3$$, A. Caprara and R. Rizzi [“Packing triangles in bounded degree graphs”, Inf. Process. Lett. 84, No. 4, 175–180 (2002; Zbl 1042.68087)] 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 $$g \in \{4,5\}$$, 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 $$g \geqslant 6$$, both problems are APX-hard already for graphs with maximum degree 3.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C38 Paths and cycles 68W25 Approximation algorithms
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##### References:
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