Packing closed trails into dense graphs
Journal of Combinatorial Theory Series B
Combinatorics, Probability and Computing
Approximation algorithms for cycle packing problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Packing directed cycles efficiently
Discrete Applied Mathematics
Approximation algorithms and hardness results for cycle packing problems
ACM Transactions on Algorithms (TALG)
Approximability of packing disjoint cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Proceedings of the forty-second ACM symposium on Theory of computing
Disjoint cycles: integrality gap, hardness, and approximation
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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It has been shown [2] that if n is odd and m1,…,mt are integers with mi⩾3 and ∑i=1t mi=|E(Kn)| then Kn can be decomposed as an edge-disjoint union of closed trails of lengths m1,…,mt. This result was later generalized [3] to all sufficiently dense Eulerian graphs G in place of Kn. In this article we consider the corresponding questions for directed graphs. We show that the complete directed graph ****gif image here**** can be decomposed as an edge-disjoint union of directed closed trails of lengths m1,…,mt whenever mi⩾2 and ****gif image here****, except for the single case when n=6 and all mi=3. We also show that sufficiently dense Eulerian digraphs can be decomposed in a similar manner, and we prove corresponding results for (undirected) complete multigraphs.