{"paper":{"title":"Interval cyclic edge-colorings of graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Petros A. Petrosyan, Sargis T. Mkhitaryan","submitted_at":"2014-11-02T18:17:01Z","abstract_excerpt":"A proper edge-coloring of a graph $G$ with colors $1,\\ldots,t$ is called an \\emph{interval cyclic $t$-coloring} if all colors are used, and the edges incident to each vertex $v\\in V(G)$ are colored by $d_{G}(v)$ consecutive colors modulo $t$, where $d_{G}(v)$ is the degree of a vertex $v$ in $G$. A graph $G$ is \\emph{interval cyclically colorable} if it has an interval cyclic $t$-coloring for some positive integer $t$. The set of all interval cyclically colorable graphs is denoted by $\\mathfrak{N}_{c}$. For a graph $G\\in \\mathfrak{N}_{c}$, the least and the greatest values of $t$ for which it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0290","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"}