{"paper":{"title":"Realizing degree sequences as $Z_3$-connected graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fan Yang, Hong -Jian Lai, Xiangwen Li","submitted_at":"2014-07-14T03:33:05Z","abstract_excerpt":"An integer-valued sequence $\\pi=(d_1, \\ldots, d_n)$ is {\\em graphic} if there is a simple graph $G$ with degree sequence of $\\pi$. We say the $\\pi$ has a realization $G$. Let $Z_3$ be a cyclic group of order three. A graph $G$ is {\\em $Z_3$-connected} if for every mapping $b:V(G)\\to Z_3$ such that $\\sum_{v\\in V(G)}b(v)=0$, there is an orientation of $G$ and a mapping $f: E(G)\\to Z_3-\\{0\\}$ such that for each vertex $v\\in V(G)$, the sum of the values of $f$ on all the edges leaving from $v$ minus the sum of the values of $f$ on the all edges coming to $v$ is equal to $b(v)$. If an integer-value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3531","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"}