Abstract
Let G=(V,E) be an undirected graph in which every vertex v∈V is assigned a nonnegative integer w(v). A w-packing is a collection 
of cycles (repetition allowed) in G such that every v∈V is contained at most w(v) times by the members of 
. Let 〈w〉=2|V|+∑
v∈V
⌈log (w(v)+1)⌉ denote the binary encoding length (input size) of the vector (w(v): v∈V)T. We present an efficient algorithm which finds in O(|V|8〈w〉2+|V|14) time a w-packing of maximum cardinality in G provided packing and covering cycles in G satisfy the ℤ+-max-flow min-cut property.
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X. Chen supported in part by the NSF of China under Grant No. 10721101, and Chinese Academy of Sciences under Grant No. kjcx-yw-s7.
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Chen, Q., Chen, X. Packing cycles exactly in polynomial time. J Comb Optim 23, 167–188 (2012). https://doi.org/10.1007/s10878-010-9347-1
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DOI: https://doi.org/10.1007/s10878-010-9347-1