{"paper":{"title":"$(3,1)^*$-choosability of planar graphs without adjacent short cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andre Raspaud, Min Chen","submitted_at":"2013-02-11T20:15:58Z","abstract_excerpt":"A list assignment of a graph $G$ is a function $L$ that assigns a list $L(v)$ of colors to each vertex $v\\in V(G)$. An $(L,d)^*$-coloring is a mapping $\\pi$ that assigns a color $\\pi(v)\\in L(v)$ to each vertex $v\\in V(G)$ so that at most $d$ neighbors of $v$ receive color $\\pi(v)$. A graph $G$ is said to be $(k,d)^*$-choosable if it admits an $(L,d)^*$-coloring for every list assignment $L$ with $|L(v)|\\ge k$ for all $v\\in V(G)$. In 2001, Lih et al. \\cite{LSWZ-01} proved that planar graphs without 4- and $l$-cycles are $(3,1)^*$-choosable, where $l\\in \\{5,6,7\\}$. Later, Dong and Xu \\cite{DX-09"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2599","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"}