{"paper":{"title":"Solving Problems on Generalized Convex Graphs via Mim-Width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Andrea Munaro, Dani\\\"el Paulusma, Flavia Bonomo-Braberman, Nick Brettell","submitted_at":"2020-08-20T14:47:54Z","abstract_excerpt":"A bipartite graph $G=(A,B,E)$ is ${\\cal H}$-convex, for some family of graphs ${\\cal H}$, if there exists a graph $H\\in {\\cal H}$ with $V(H)=A$ such that the set of neighbours in $A$ of each $b\\in B$ induces a connected subgraph of $H$. Many $\\mathsf{NP}$-complete problems, including problems such as Dominating Set, Feedback Vertex Set, Induced Matching and List $k$-Colouring, become polynomial-time solvable for ${\\mathcal H}$-convex graphs when ${\\mathcal H}$ is the set of paths. In this case, the class of ${\\mathcal H}$-convex graphs is known as the class of convex graphs. The underlying rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.09004","kind":"arxiv","version":4},"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/2008.09004/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"}