Unifying Duality Theorems for Width Parameters in Graphs and Matroids (Extended Abstract)
We prove a general duality theorem for width parameters in combinatorial structures such as graphs and matroids. It implies the classical such theorems for path-width, tree-width, branch-width and rank-width, and gives rise to new width parameters with associated duality theorems. The dense substructures witnessing large width are presented in a unified way akin to tangles, as orientations of separation systems satisfying certain consistency axioms.
KeywordsDuality Theorem Separation System Width Parameter Order Function Connectivity Function
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