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

Authors:
Xujin Chen;Guoli Ding;Wenan Zang
Affiliations:
Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China;Mathematics Department, Louisiana State University, Baton Rouge, LA, USA;Department of Mathematics, The University of Hong Kong, Hong Kong, China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Let G be a graph and let A be its cutset-edge incidence matrix. We prove that the linear system 12Ax=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 Cornuejols, Fonlupt, and Naddef and by Mahjoub which assert that both polyhedra {x|12Ax=1,x=0} and {x|12Ax=1,1=x=0} are integral if G is series-parallel.