{"paper":{"title":"Z_2-genus of graphs and minimum rank of partial symmetric matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Jan Kyn\\v{c}l, Radoslav Fulek","submitted_at":"2019-03-20T17:50:59Z","abstract_excerpt":"The \\emph{genus} $\\mathrm{g}(G)$ of a graph $G$ is the minimum $g$ such that $G$ has an embedding on the orientable surface $M_g$ of genus $g$.\n  A drawing of a graph on a surface is \\emph{independently even} if every pair of nonadjacent edges in the drawing crosses an even number of times. The \\emph{$\\mathbb{Z}_2$-genus} of a graph $G$, denoted by $\\mathrm{g}_0(G)$, is the minimum $g$ such that $G$ has an independently even drawing on $M_g$.\n  By a result of Battle, Harary, Kodama and Youngs from 1962, the graph genus is additive over 2-connected blocks.\n  In 2013, Schaefer and \\v{S}tefankovi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08637","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"}