Unifying duality theorems for width parameters in graphs and matroids. I. Weak and strong duality
Reinhard Diestel, Sang‐il Oum · arXiv (Cornell University) · 2014
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 highly connected substructures witnessing large width are presented in a unified way akin to tangles, as orientations of low-order separations satisfying certain consistency axioms.