{"paper":{"title":"Hyperbolicity of direct products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alvaro Mart\\'inez-P\\'erez, Amauris de la Cruz, Jos\\'e M. Rodr\\'iguez, Walter Carballosa","submitted_at":"2016-11-14T13:03:17Z","abstract_excerpt":"If $X$ is a geodesic metric space and $x_1,x_2,x_3\\in X$, a {\\it geodesic triangle} $T=\\{x_1,x_2,x_3\\}$ is the union of the three geodesics $[x_1x_2]$, $[x_2x_3]$ and $[x_3x_1]$ in $X$. The space $X$ is $\\delta$-\\emph{hyperbolic} $($in the Gromov sense$)$ if any side of $T$ is contained in a $\\delta$-neighborhood of the union of the two other sides, for every geodesic triangle $T$ in $X$. If $X$ is hyperbolic, we denote by $\\delta(X)$ the sharp hyperbolicity constant of $X$, i.e., $\\delta(X)=\\inf\\{\\delta\\ge 0: \\, X \\, \\text{ is $\\delta$-hyperbolic}\\,\\}.$ Some previous works characterize the hy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04372","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"}