{"paper":{"title":"Solutions for two conjectures on kaleidoscopic edge-colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiaoyu Zhu, Xueliang Li","submitted_at":"2016-11-24T05:03:15Z","abstract_excerpt":"For an $r$-regular graph $G$, we define an edge-coloring $c$ with colors from $\\{1,2,\\cdots,$ $k\\}$, in such a way that any vertex of $G$ is incident to at least one edge of each color. The multiset-color $c_m(v)$ of a vertex $v$ is defined as the ordered tuple $(a_1,a_2,\\cdots ,a_k)$, where $a_i \\ (1\\leq i\\leq k)$ denotes the number of edges with color $i$ which are incident with $v$ in $G$. Then this edge-coloring $c$ is called a {\\it $k$-kaleidoscopic coloring} of $G$ if every two distinct vertices in $G$ have different multiset-colors and in this way the graph $G$ is defined as a {\\it $k$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08068","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"}