Packing and covering with linear programming: A survey

This paper considers the polyhedral results and the min–max results on packing and covering problems of the decade. Since the strong perfect graph theorem (published in 2006), the main such results are available for the packing problem, however there are still important polyhedral questions that remain open. For the covering problem, the main questions are still open, although there has been important progress. We survey some of the main results with emphasis on those where linear programming and graph theory come together. They mainly concern the covering of cycles or dicycles in graphs or signed graphs, either with vertices or edges; this includes the multicut and integral multiflow problems.

► Min–max and polyhedral results on packing-covering (survey: 2000–2010). ► Perfect matrices, stable set polytope. ► Ideal and Mengerian matrices, Seymour’s conjecture. ► Max-multiow/min-multicut. ► Cycles and dicycles in graphs.