{"paper":{"title":"Some Results on Cyclic Interval Edge Colorings of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Armen S. Asratian, Carl Johan Casselgren, Petros A. Petrosyan","submitted_at":"2016-06-30T08:34:53Z","abstract_excerpt":"A proper edge coloring of a graph $G$ with colors $1,2,\\dots,t$ is called a \\emph{cyclic interval $t$-coloring} if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is considered as consecutive to color $t$. We prove that a bipartite graph $G$ with even maximum degree $\\Delta(G)\\geq 4$ admits a cyclic interval $\\Delta(G)$-coloring if for every vertex $v$ the degree $d_G(v)$ satisfies either $d_G(v)\\geq \\Delta(G)-2$ or $d_G(v)\\leq 2$. We also prove that every Eulerian bipartite graph $G$ with maximum degree at most $8$ has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09389","kind":"arxiv","version":2},"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"}