Document Type
Article
Publication Date
1-1-2002
Abstract
A graph G is called cycle Mengerian (CM) if for all nonnegative integral function w defined on V(G), the maximum number of cycles (repetition is allowed) in G such that each vertex v is used at most w(v) times is equal to the minimum of ∑ {w(x) : x ∈ X}, where the minimum is taken over all X ⊆ V(G) such that deleting X from G results in a forest. The purpose of this paper is to characterize all CM graphs in terms of forbidden structures. As a corollary, we prove that if the fractional version of the above minimization problem always have an integral optimal solution, then the fractional version of the maximization problem will always have an integral optimal solution as well. 2002 Elsevier Science (USA).
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
First Page
381
Last Page
407
Recommended Citation
Ding, G., & Zang, W. (2002). Packing cycles in graphs. Journal of Combinatorial Theory. Series B, 86 (2), 381-407. https://doi.org/10.1006/jctb.2002.2134