{"paper":{"title":"Every signed planar graph is $5$-choosable: A short proof and refinements","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maxwell Ndognkon Manga, Pie Desire Ebode Atangana","submitted_at":"2026-05-19T16:24:20Z","abstract_excerpt":"A \\emph{signed graph} is a pair $\\Gs$ in which $G$ is a finite simple graph and $\\sigma:\\E(G)\\to\\{+1,-1\\}$ is a \\emph{signature}. Following M\\'a\\v{c}ajov\\'a--Raspaud- \\v{S}koviera and Jin--Kang--Steffen, a \\emph{proper coloring} of $\\Gs$ is a map $c:\\V(G)\\to\\Z$ with $c(u)\\ne\\sigma(uv)\\,c(v)$ for every edge $uv$, and $\\Gs$ is \\emph{signed $k$-choosable} if such a coloring exists from any list assignment $L$ with $|L(v)|\\ge k$. In a celebrated two-page note, Thomassen proved that every planar graph is $5$ choosable, and Jin, Kang, and Steffen subsequently extended this to signed planar graphs. O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22860","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22860/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}