{"paper":{"title":"The (1,2)-step competition graph of a hypertournament","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruijuan Li, Xiaoting An, Xinhong Zhang","submitted_at":"2018-12-05T03:12:18Z","abstract_excerpt":"Competition graphs were created in connected to a biological model as a means of reflecting the competition relations among the predators in the food webs and determining the smallest dimension of ecological phase space. In 2011, Factor and Merz introduced the (1,2)-step competition graph of a digraph. Given a digraph $D=(V,A)$, the (1,2)-step competition graph of $D$, denoted $C_{1,2}(D)$, is a graph on $V(D)$ where $xy\\in E(C_{1,2}(D))$ if and only if there exists a vertex $z\\neq x,y$ such that either $d_{D-y}(x,z)=1$ and $d_{D-x}(y,z)\\leq 2$ or $d_{D-x}(y,z)=1$ and $d_{D-y}(x,z)\\leq 2$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01796","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"}