This workshop, sponsored by AIM and the NSF, is motivated by questions related to structural complexity of graphs. A "width" parameter measures the structural complexity of a graph by comparing its "thickness" to specific graphs designated as the "thinnest." Graphs of small width exhibit particularly favorable structural and algorithmic properties. In the last decade a considerable effort was directed to the study of width parameters — such as treewidth, tree-independence number, twin-width, and others — in graph classes defined by forbidding certain induced subgraphs and induced minors. Many novel techniques were developed; some of these techniques tend to be applicable to other topics, particularly the emerging area of coarse graph theory.

This workshop will focus on several research directions that fall into this category, as follows.

1. Bounding graph width parameters (treewidth, tree-independence number, twin width and others) in graph families defined by forbidden induced substructures.
2. Coarse graph theory, with focus on the induced versions of Menger Theorem.
3. Variants of the Erdös-Pósa property with focus on induced and coarse regimes.