Theory of linear and integer programming
Theory of linear and integer programming
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Journal of Combinatorial Theory Series B
A Min-Max Relation on Packing Feedback Vertex Sets
Mathematics of Operations Research
A min-max relation on packing feedback vertex sets
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
An efficient algorithm for finding maximum cycle packings in reducible flow graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Packing cycles exactly in polynomial time
Journal of Combinatorial Optimization
On the feedback vertex set polytope of a series-parallel graph
Discrete Optimization
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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 υ is used at most w(υ) times is equal to the minimum of Σ{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.