{"paper":{"title":"A note on the Erd\\\"os-Faber-Lov\\'asz Conjecture: quasigroups and complete digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adrian Vazquez-Avila, Christian Rubio-Montiel, Gabriela Araujo-Pardo","submitted_at":"2015-08-22T17:29:05Z","abstract_excerpt":"A decomposition of a simple graph $G$ is a pair $(G,P)$ where $P$ is a set of subgraphs of $G$, which partitions the edges of $G$ in the sense that every edge of $G$ belongs to exactly one subgraph in $P$. If the elements of $P$ are induced subgraphs then the decomposition is denoted by $[G,P]$.\n  A $k$-$P$-coloring of a decomposition $(G,P)$ is a surjective function that assigns to the edges of $G$ a color from a $k$-set of colors, such that all edges of $H\\in P$ have the same color, and, if $H_1,H_2\\in P$ with $V(H_1)\\cap V(H_2)\\neq\\emptyset$ then $E(H_1)$ and $E(H_2)$ have different colors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05532","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"}