{"paper":{"title":"Caterpillars in Erd\\H{o}s-Hajnal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anita Liebenau, Marcin Pilipczuk, Paul Seymour, Sophie Spirkl","submitted_at":"2018-10-01T16:48:52Z","abstract_excerpt":"Let $T$ be a tree such that all its vertices of degree more than two lie on one path, that is, $T$ is a caterpillar subdivision. We prove that there exists $\\epsilon>0$ such that for every graph $G$ with $|V(G)|\\ge 2$ not containing $T$ as an induced subgraph, either some vertex has at least $\\epsilon|V(G)|$ neighbours, or there are two disjoint sets of vertices $A,B$, both of cardinality at least $\\epsilon|V(G)|$, where there is no edge joining $A$ and $B$.\n  A consequence is: for every caterpillar subdivision $T$, there exists $c>0$ such that for every graph $G$ containing neither of $T$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00811","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}