Maria Chudnovsky, Induced subgraphs and tree decompositions

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Tree decompositions are a powerful tool in structural graph theory; they are traditionally used in the context of forbidden graph minors. Connecting tree decompositions and forbidden induced subgraphs has until recently remained out of reach. Tree decompositions are closely related to the existence of "laminar collections of separations" in a graph, which roughly means that

Maria Chudnovsky, Induced subgraphs and tree decompositions

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Tree decompositions are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. Tree decompositions

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