{"paper":{"title":"Forcing monochromatic induced subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sepehr Hajebi, Sophie Spirkl","submitted_at":"2026-06-23T15:23:37Z","abstract_excerpt":"We prove that for all $c\\in\\mathbb N$ and nonnull graphs $H_1,\\ldots,H_t$, there exists $n\\in\\mathbb N$ such that if $G$ is a $c$-edge-colored complete graph with no monochromatic induced copy of the complete join of $H_1,\\ldots,H_t$, then $V(G)$ is the union of $n$ sets $V_1,\\ldots,V_n$ such that within each set $V_j$ with $|V_j|\\neq 1$, the edges of some color form a graph that excludes at least one of $H_1,\\ldots,H_t$ as an induced subgraph. In fact, the same holds even if the colors overlap, and with a different list of graphs $H_1,\\ldots,H_t$ assigned to each color. When $H_1,\\ldots,H_t$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24695","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/2606.24695/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"}