Scott, AlexSeymour, PaulSpirkl, Sophie2024-02-092024-02-092024https://doi.org/10.1137/21m1456509http://hdl.handle.net/10012/20340(c) Society for Industrial and Applied Mathematics. Scott, A., Seymour, P., & Spirkl, S. T. (2024a). Pure pairs. ix. transversal trees. SIAM Journal on Discrete Mathematics, 38(1), 645–667. https://doi.org/10.1137/21m1456509Fix k>0, and let G be a graph, with vertex set partitioned into k subsets ("blocks") of approximately equal size. An induced subgraph of G is "transversal" (with respect to this partition) if it has exactly one vertex in each block (and therefore it has exactly k vertices). A "pure pair" in G is a pair X,Y of disjoint subsets of V(G) such that either all edges between X,Y are present or none are; and in the present context we are interested in pure pairs (X,Y) where each of X,Y is a subset of one of the blocks, and not the same block. This paper collects several results and open questions concerning how large a pure pair must be present if various types of transversal subgraphs are excluded.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/induced subgraphstreespure pairsArticle