{"paper":{"title":"Examples of cyclically-interval non-colorable bipartite graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"R.R. Kamalian","submitted_at":"2013-05-29T16:53:38Z","abstract_excerpt":"For an undirected, simple, finite, connected graph $G$, we denote by $V(G)$ and $E(G)$ the sets of its vertices and edges, respectively. A function $\\varphi:E(G)\\rightarrow\\{1,2,\\ldots,t\\}$ is called a proper edge $t$-coloring of a graph $G$ if adjacent edges are colored differently and each of $t$ colors is used. An arbitrary nonempty subset of consecutive integers is called an interval. If $\\varphi$ is a proper edge $t$-coloring of a graph $G$ and $x\\in V(G)$, then $S_G(x,\\varphi)$ denotes the set of colors of edges of $G$ which are incident with $x$. A proper edge $t$-coloring $\\varphi$ of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6866","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"}