{"paper":{"title":"A parity Erd\\H{o}s-Hajnal theorem for $t$-intersecting curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Suk, Su Zhou","submitted_at":"2026-06-10T04:27:18Z","abstract_excerpt":"For every fixed $t\\ge 1$, we prove a parity analogue of the mighty Erd\\H{o}s-Hajnal property for $t$-intersecting curves in the plane. Let $\\mathcal B$ be a set of blue curves and $\\mathcal G$ a set of green curves in the plane such that $\\mathcal B\\cup\\mathcal G$ is a collection of $t$-intersecting curves in general position. We show that there exist subfamilies $\\mathcal B'\\subseteq\\mathcal B$ and $\\mathcal G'\\subseteq\\mathcal G$ such that $|\\mathcal B'|\\geq \\varepsilon|\\mathcal B|$ and $|\\mathcal G'|\\geq \\varepsilon|\\mathcal G|$, where $\\varepsilon>0$ depends only on $t$, such that either e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11649","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11649/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"}