{"paper":{"title":"Color-blind index in graphs of very low degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charlie Suer, Derrick Stolee, Devon Sigler, Jennifer Diemunsch, Lauren M. Nelsen, Lucas Kramer, Luke L. Nelsen, Nathan Graber, Victor Larsen","submitted_at":"2015-06-28T02:08:56Z","abstract_excerpt":"Let $c:E(G)\\to [k]$ be an edge-coloring of a graph $G$, not necessarily proper. For each vertex $v$, let $\\bar{c}(v)=(a_1,\\ldots,a_k)$, where $a_i$ is the number of edges incident to $v$ with color $i$. Reorder $\\bar{c}(v)$ for every $v$ in $G$ in nonincreasing order to obtain $c^*(v)$, the color-blind partition of $v$. When $c^*$ induces a proper vertex coloring, that is, $c^*(u)\\neq c^*(v)$ for every edge $uv$ in $G$, we say that $c$ is color-blind distinguishing. The minimum $k$ for which there exists a color-blind distinguishing edge coloring $c:E(G)\\to [k]$ is the color-blind index of $G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08345","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"}