{"paper":{"title":"Trees, ladders and graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"D\\'aniel T. Soukup","submitted_at":"2014-09-09T23:50:55Z","abstract_excerpt":"We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erd\\H{o}s and A. Hajnal from 1985, we construct graphs of chromatic number $\\omega_1$ without uncountable $\\omega$-connected subgraphs. Second, we build triangle free graphs of chromatic number $\\omega_1$ without subgraphs isomorphic to $H_{\\omega,\\omega+2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2922","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"}