{"paper":{"title":"Silver block intersection graphs of Steiner 2-designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Ahadi, E. S. Mahmoodian, M. Mortezaeefar, Nazli Besharati","submitted_at":"2010-05-25T07:23:11Z","abstract_excerpt":"For a block design $\\cal{D}$, a series of {\\sf block intersection graphs} $G_i$, or $i$-{\\rm BIG}($\\cal{D}$), $i=0, ..., k$ is defined in which the vertices are the blocks of $\\cal{D}$, with two vertices adjacent if and only if the corresponding blocks intersect in exactly $i$ elements. A silver graph $G$ is defined with respect to a maximum independent set of $G$, called a {\\sf diagonal} of that graph. Let $G$ be $r$-regular and $c$ be a proper $(r + 1)$-coloring of $G$. A vertex $x$ in $G$ is said to be {\\sf rainbow} with respect to $c$ if every color appears in the closed neighborhood $N[x]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4492","kind":"arxiv","version":3},"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"}