Theory of linear and integer programming
Theory of linear and integer programming
A generalization of a graph result of D. W. Hall
Discrete Mathematics
A characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
Ideal Binary Clutters, Connectivity, and a Conjecture of Seymour
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
Single commodity-flow algorithms for lifts of graphic and co-graphic matroids
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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A family of sets H is ideal if the polyhedron {x =0 : ? i?S x i= 1, ?S脗 脗 ? H} is integral. Consider a graphG with verticess,t. Anodd st-walk is either an oddst-path or the union of an evenst-path and an odd circuit that share, at most, one vertex. Let T be a subset of vertices of even cardinality. Anst-T-cut脗 脗 is a cut of the form d( U) where |U? T | is odd andU contains exactly one ofs ort. We give excluded minor characterizations for when the families of oddst-walks andst- T-cuts (represented as sets of edges) are ideal. As a corollary, we characterize which extensions and coextensions of graphic and cographic matroids are 1-flowing.