{"paper":{"title":"A graph minors characterization of signed graphs whose signed Colin de Verdi\\`ere parameter $\\nu$ is two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frank J. Hall, Hein van der Holst, Marina Arav, Zhongshan Li","submitted_at":"2012-09-20T19:39:20Z","abstract_excerpt":"A signed graph is a pair $(G,\\Sigma)$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V=\\{1,...,n\\}$ and $\\Sigma\\subseteq E$. The edges in $\\Sigma$ are called odd and the other edges even. By $S(G,\\Sigma)$ we denote the set of all symmetric $n\\times n$ matrices $A=[a_{i,j}]$ with $a_{i,j}<0$ if $i$ and $j$ are connected by only even edges, $a_{i,j}>0$ if $i$ and $j$ are connected by only odd edges, $a_{i,j}\\in \\mathbb{R}$ if $i$ and $j$ are connected by both even and odd edges, $a_{i,j}=0$ if $i\\not=j$ and $i$ and $j$ are non-adjacent, and $a_{i,i} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4628","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"}