{"paper":{"title":"Excluding a large theta graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emily Marshall, Guoli Ding","submitted_at":"2016-09-05T16:53:20Z","abstract_excerpt":"A theta graph, denoted $\\theta_{a,b,c}$, is a graph of order $a+b+c-1$ consisting of a pair of vertices and three independent paths between them of lengths $a$, $b$, and $c$. We provide a complete characterization of graphs that do not contain a large $\\theta_{a,b,c}$ as a topological minor. More specifically, we describe the structure of $\\theta_{1,2,t}$-, $\\theta_{2,2,t}$-, $\\theta_{1,t,t}$-, $\\theta_{2,t,t}$-, and $\\theta_{t,t,t}$-free graphs where $t$ is large. The main result is a characterization of $\\theta_{t,t,t}$-free graphs for large $t$. The $3$-connected $\\theta_{t,t,t}$-free graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01221","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"}