Tutte Colloquium -Jim Geelen-Tangles in graphs and matroids

Abstract: A common strategy in many proofs and algorithms is to begin by decomposing a graph into more highly connected pieces. Decomposition is easy when the goal is to obtain connected or 2-connected pieces, and decomposition into 3- or 4-connected pieces is also straightforward in many settings. For higher levels of connectivity, however, no effective and widely applicable notion of decomposition is currently known. To address this, Robertson and Seymour introduced tangles, which capture the k-connected regions of a graph without decomposing.