{"paper":{"title":"List colouring of graphs and generalized Dyck paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rongxing Xu, Xuding Zhu, Yeong-Nan Yeh","submitted_at":"2017-11-08T07:31:02Z","abstract_excerpt":"The Catalan numbers occur in various counting problems in combinatorics. This paper reveals a connection between the Catalan numbers and list colouring of graphs. Assume $G$ is a graph and $f:V(G) \\to N$ is a mapping. For a nonnegative integer $m$, let $f^{(m)}$ be the extension of $f$ to the graph $ G \\diamondplus \\overline{K_m}$ for which $f^{(m)}(v)=|V(G)|$ for each vertex $v$ of $\\overline{K_m}$. Let $m_c(G,f)$ be the minimum $m$ such that $ G \\diamondplus \\overline{K_m}$ is not $f^{(m)}$-choosable and $m_p(G,f)$ be the minimum $m$ such that $ G \\diamondplus \\overline{K_m}$ is not $f^{(m)}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02852","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"}