{"paper":{"title":"The phylogeny number in the aspect of triangles and diamonds of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hojun Lee, Soogang Eoh, Suh-Ryung Kim","submitted_at":"2019-04-16T02:49:59Z","abstract_excerpt":"Given an acyclic digraph $D$, the competition graph of $D$, denoted by $C(D)$, is the simple graph having vertex set $V(D)$ and edge set $\\{uv \\mid (u, w), (v, w) \\in A(D) \\text{ for some } w \\in V(D) \\}$. The phylogeny graph of an acyclic digraph $D$, denoted by $P(D)$, is the graph with the vertex set $V(D)$ and the edge set $E(U(D)) \\cup E(C(D))$ where $U(D)$ denotes the underlying graph of $D$. The notion of phylogeny graphs was introduced by Roberts and Sheng~\\cite{roberts1997phylogeny} as a variant of competition graph. Moral graphs having arisen from studying Bayesian networks are the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07420","kind":"arxiv","version":2},"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"}