{"paper":{"title":"Total weight choosability for Halin graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tsai-Lien Wong, Xuding Zhu, Yu-Chang Liang","submitted_at":"2017-05-23T09:34:04Z","abstract_excerpt":"A proper total weighting of a graph $G$ is a mapping $\\phi$ which assigns to each vertex and each edge of $G$ a real number as its weight so that for any edge $uv$ of $G$, $\\sum_{e \\in E(v)}\\phi(e)+\\phi(v) \\ne \\sum_{e \\in E(u)}\\phi(e)+\\phi(u)$. A $(k,k')$-list assignment of $G$ is a mapping $L$ which assigns to each vertex $v$ a set $L(v)$ of $k$ permissible weights and to each edge $e$ a set $L(e)$ of $k'$ permissible weights. An $L$-total weighting is a total weighting $\\phi$ with $\\phi(z) \\in L(z)$ for each $z \\in V(G) \\cup E(G)$. A graph $G$ is called $(k,k')$-choosable if for every $(k,k'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08150","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"}