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On Packing Edge-Disjoint Cycles in Digraphs and Its Applications in Connectivity Problems

DOI: 10.4236/ojdm.2026.164005, PP. 49-64

Keywords: Directed Graphs, Cycle Packing, Node Connectivity, Approximation Algorithms

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Abstract:

We consider the problem of packing edge-disjoint cycles in digraphs. It is shown that for k=2,3 , any digraph with minimum degree k contains at least k+1 edge-disjoint directed cycles of size ≥k . In each of these two cases, examples are given to show that k+1 edge-disjoint directed cycles is the best we can achieve. These results are applied to obtain approximation algorithms for k -node-connectivity problems.

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