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Learn about tree decompositions and path decompositions in graph theory through this academic lecture that explores their role in structural graph theory and algorithms. Delve into how these powerful tools make complex problems more manageable when input graphs have bounded "width" tree decompositions. Examine the complete characterization of bounded treewidth and pathwidth families through forbidden subgraphs and minors from the 1990s, and discover new research connecting these concepts to local graph containment relations like induced subgraphs and induced minors. Explore recent findings that provide a comprehensive list of induced subgraph obstructions to bounded pathwidth, based on collaborative work with Sepehr Hajebi and Sophie Spirkl, which builds upon an extensive series of 18 papers on induced subgraphs and tree decompositions.
