Results 1 
2 of
2
Packing Odd Circuits in Eulerian Graphs
 Journal of Combinatorial Theory, Series B
"... Let C be the clutter of odd circuits of a signed graph (G; ). For nonnegative integral edge{weights w, we are interested in the linear program min(w t x : x(C) 1; for C 2 C; and x 0), which we denote by (P ). Solving the related integer program is clearly equivalent to the maximum cut problem, ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Let C be the clutter of odd circuits of a signed graph (G; ). For nonnegative integral edge{weights w, we are interested in the linear program min(w t x : x(C) 1; for C 2 C; and x 0), which we denote by (P ). Solving the related integer program is clearly equivalent to the maximum cut problem, which is NP{hard. Guenin proved that (P ) has an optimal solution that is integral so long as (G; ) does not contain a minor isomorphic to odd{K 5 . We generalize this by showing that, if (G; ) does not contain a minor isomorphic to odd{K 5 then (P ) has an integral optimal solution and its dual has a half{integral optimal solution. 1.
A Characterization of BoxMengerian Matroid Ports
"... Let M be a matroid on E ∪ {`}, where ` 6 ∈ E is a distinguished element of M. The `port of M is the set P = {P: P ⊆ E with P ∪ {`} a circuit of M}. Let A be the PE incidence matrix. Let U2,4 be the uniform matroid on four elements of rank two, F7 be the Fano matroid, F 7 be the dual of F7, and F+7 ..."
Abstract
 Add to MetaCart
Let M be a matroid on E ∪ {`}, where ` 6 ∈ E is a distinguished element of M. The `port of M is the set P = {P: P ⊆ E with P ∪ {`} a circuit of M}. Let A be the PE incidence matrix. Let U2,4 be the uniform matroid on four elements of rank two, F7 be the Fano matroid, F 7 be the dual of F7, and F+7 be the unique series extension of F7. In this paper, we prove that the system Ax ≥ 1, x ≥ 0 is boxtotally dual integral (boxTDI) if and only if M has no U2,4minor using `, no F 7minor using `, and no F+7minor using ` as a series element. Our characterization yields a number of interesting results in combinatorial optimization.