{"paper":{"title":"Non-monochromatic Triangles in a 2-Edge-Coloured Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Montejano, Jessica McDonald, Matt DeVos","submitted_at":"2018-09-26T15:59:27Z","abstract_excerpt":"Let $G = (V,E)$ be a simple graph and let $\\{R,B\\}$ be a partition of $E$. We prove that whenever $|E| + \\min\\{ |R|, |B| \\} > { |V| \\choose 2 }$, there exists a subgraph of $G$ isomorphic to $K_3$ which contains edges from both $R$ and $B$. We conjecture a natural generalization to partitions with more blocks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10088","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"}