{"paper":{"title":"On (4,2)-Choosable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gregory J. Puleo, Jixian Meng, Xuding Zhu","submitted_at":"2014-04-27T20:25:15Z","abstract_excerpt":"A graph $G$ is called $(a,b)$-choosable if for any list assignment $L$ which assigns to each vertex $v$ a set $L(v)$ of $a$ permissible colours, there is a $b$-tuple $L$-colouring of $G$. An $(a,1)$-choosable graph is also called $a$-choosable. In the pioneering paper on list colouring of graphs by Erd\\H{o}s, Rubin and Taylor, $2$-choosable graphs are characterized. Confirming a special case of a conjecture of Erd\\H{o}s--Rubin--Taylor, Tuza and Voigt proved that $2$-choosable graphs are $(2m,m)$-choosable for any positive integer $m$. On the other hand, Voigt proved that if $m$ is an odd integ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6821","kind":"arxiv","version":3},"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"}