Pure Pairs. IX. Transversal Trees
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Date
2024
Authors
Scott, Alex
Seymour, Paul
Spirkl, Sophie
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Abstract
Fix 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.
Description
(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/10.1137/21m1456509
Keywords
induced subgraphs, trees, pure pairs