{"paper":{"title":"Degree choosable signed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Stiebitz, Thomas Schweser","submitted_at":"2015-07-16T13:42:15Z","abstract_excerpt":"A signed graph is a graph in which each edge is labeled with $+1$ or $-1$. A (proper) vertex coloring of a signed graph is a mapping $\\f$ that assigns to each vertex $v\\in V(G)$ a color $\\f(v)\\in \\mz$ such that every edge $vw$ of $G$ satisfies $\\f(v)\\not= \\sg(vw)\\f(w)$, where $\\sg(vw)$ is the sign of the edge $vw$. For an integer $h\\geq 0$, let $\\Ga_{2h}=\\{\\pm1,\\pm2, \\ldots, \\pm h\\}$ and $\\Ga_{2h+1}=\\Ga_{2h} \\cup \\{0\\}$. Following \\cite{MaRS2015}, the signed chromatic number $\\scn(G)$ of $G$ is the least integer $k$ such that $G$ admits a vertex coloring $\\f$ with ${\\rm im}(\\f)\\subseteq \\Ga_k$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04569","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"}