{"paper":{"title":"Excluding a clique or a biclique in graphs of bounded induced matching treewidth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bartosz Walczak, Jadwiga Czy\\.zewska, Marcin Bria\\'nski, Martin Milani\\v{c}, Pawe{\\l} Rz\\k{a}\\.zewski, Rose McCarty, Tara Abrishami","submitted_at":"2024-05-07T19:01:16Z","abstract_excerpt":"For a tree decomposition $\\mathcal{T}$ of a graph $G$, let $\\mu(\\mathcal{T})$ denote the maximum size of an induced matching in $G$ with the property that some bag of $\\mathcal{T}$ contains at least one endpoint of every edge of the matching. The induced matching treewidth of a graph $G$ is the minimum value of $\\mu(\\mathcal{T})$ over all tree decompositions $\\mathcal{T}$ of $G$. Classes of graphs with bounded induced matching treewidth admit polynomial-time algorithms for a number of problems, including INDEPENDENT SET, $k$-COLORING, ODD CYCLE TRANSVERSAL, and FEEDBACK VERTEX SET. In this pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04617","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04617/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}