{"paper":{"title":"Conditions on square geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Huda Chuangpishit, Jeannette Janssen","submitted_at":"2016-10-24T16:06:31Z","abstract_excerpt":"For any metric $d$ on $\\mathbb{R}^2$, an ($\\mathbb{R}^2,d$)-geometric graph is a graph whose vertices are points in $\\mathbb{R}^2$, and two vertices are adjacent if and only if their distance is at most 1. If $d=\\|.\\|_{\\infty}$, the metric derived from the $L_{\\infty}$ norm, then $(\\mathbb{R} ^2,\\|.\\|_{\\infty})$-geometric graphs are precisely those graphs that are the intersection of two unit interval graphs. We refer to $(\\mathbb{R}^2,\\|.\\|_{\\infty})$-geometric graphs as square geometric graphs. We represent a characterization of square geometric graphs. Using this characterization we provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07468","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"}