Add to ORKGThe purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: for any nonnegative integral weight function w defined on E(M), Maximum { k: M has k circuits ,(repetition, allowed) such that each element e of M is used at most 2w(e) times by these circuits = Minimum { ∑x ∈ X w(x): X is a collection of elements (repetition allowed) of M such that every circuit in M meets X at least twice}. Our characterization contains a complete solution to a research problem on 2-edge-connected subgraph polyhedra posed by Cornuéjols, Fonlupt, and Naddef in 1985, which was independently solved by Vandenbussche and Nemhauser in Vandenbussche and Nemhauser (J. Comb. Optim. 9:357-379, 2005). © 2008 Springer-Verlag
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M , the sum of the maxim...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
The max-flow min-cut theorem and the two-commodity flow theorem may both be interpreted as equalitie...
The purpose of this paper is to characterize all matroids M that satisfy the following minimax relat...
AbstractIn 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the...
AbstractWe prove a conjecture of Welsh, that for every matroid M without coloops, ν(M) + θ(M) ≤ ϱ(M)...
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the maximum...
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the maximum...
AbstractA matroid has the max-flow min-cut property if a certain circuit packing problem has an opti...
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, ...
AbstractWe verify a conjecture regarding circuits of a binary matroid. Acircuit coverof a integer-we...
Let M be a matroid on E ∪ {l}, where l ∉ E is a distinguished element of M. The l-port of M is the s...
AbstractLet n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this...
AbstractA matroid has the Fulkerson property with respect to a fixed element ē if equality exists b...
AbstractLet G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear sys...
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M , the sum of the maxim...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
The max-flow min-cut theorem and the two-commodity flow theorem may both be interpreted as equalitie...
The purpose of this paper is to characterize all matroids M that satisfy the following minimax relat...
AbstractIn 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the...
AbstractWe prove a conjecture of Welsh, that for every matroid M without coloops, ν(M) + θ(M) ≤ ϱ(M)...
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the maximum...
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M, the sum of the maximum...
AbstractA matroid has the max-flow min-cut property if a certain circuit packing problem has an opti...
Let n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this paper, ...
AbstractWe verify a conjecture regarding circuits of a binary matroid. Acircuit coverof a integer-we...
Let M be a matroid on E ∪ {l}, where l ∉ E is a distinguished element of M. The l-port of M is the s...
AbstractLet n be an integer exceeding one and M be a matroid having at least n + 2 elements. In this...
AbstractA matroid has the Fulkerson property with respect to a fixed element ē if equality exists b...
AbstractLet G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear sys...
In 1981, Seymour proved a conjecture of Welsh that, in a connected matroid M , the sum of the maxim...
Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of siz...
The max-flow min-cut theorem and the two-commodity flow theorem may both be interpreted as equalitie...