{"paper":{"title":"Induced cycles in triangle graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aparna Lakshmanan S., Csilla Bujt\\'as, Zsolt Tuza","submitted_at":"2014-10-31T16:55:44Z","abstract_excerpt":"The triangle graph of a graph $G$, denoted by ${\\cal T}(G)$, is the graph whose vertices represent the triangles ($K_3$ subgraphs) of $G$, and two vertices of ${\\cal T}(G)$ are adjacent if and only if the corresponding triangles share an edge. In this paper, we characterize graphs whose triangle graph is a cycle and then extend the result to obtain a characterization of $C_n$-free triangle graphs. As a consequence, we give a forbidden subgraph characterization of graphs $G$ for which ${\\cal T}(G)$ is a tree, a chordal graph, or a perfect graph. For the class of graphs whose triangle graph is p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8807","kind":"arxiv","version":3},"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"}