#### Title

The box-TDI system associated with 2-edge connected spanning subgraphs

#### Document Type

Article

#### Publication Date

1-6-2009

#### Abstract

Let G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear system frac(1, 2) A x ≥ 1, x ≥ 0 is box totally dual integral (box-TDI) if and only ifG is a series-parallel graph; a by-product of this characterization is a structural description of a box-TDI system on matroids. Our results strengthen two previous theorems obtained respectively by Cornuéjols, Fonlupt, and Naddef and by Mahjoub which assert that both polyhedra {x {divides} frac(1, 2) A x ≥ 1, x ≥ 0} and {x {divides} frac(1, 2) A x ≥ 1, 1 ≥ x ≥ 0} are integral if G is series-parallel. © 2008 Elsevier B.V. All rights reserved.

#### Publication Source (Journal or Book title)

Discrete Applied Mathematics

#### First Page

118

#### Last Page

125

#### Recommended Citation

Chen, X., Ding, G., & Zang, W.
(2009). The box-TDI system associated with 2-edge connected spanning subgraphs.* Discrete Applied Mathematics**, 157* (1), 118-125.
https://doi.org/10.1016/j.dam.2008.05.001