{"paper":{"title":"Graph Homomorphisms via Vector Colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antonios Varvitsiotis, Brendan Rooney, Chris Godsil, David E. Roberson, Robert \\v{S}\\'amal","submitted_at":"2016-10-31T16:30:08Z","abstract_excerpt":"In this paper we study the existence of homomorphisms $G\\to H$ using semidefinite programming. Specifically, we use the vector chromatic number of a graph, defined as the smallest real number $t \\ge 2$ for which there exists an assignment of unit vectors $i\\mapsto p_i$ to its vertices such that $\\langle p_i, p_j\\rangle\\le -1/(t-1),$ when $i\\sim j$. Our approach allows to reprove, without using the Erd\\H{o}s-Ko-Rado Theorem, that for $n>2r$ the Kneser graph $K_{n:r}$ and the $q$-Kneser graph $qK_{n:r}$ are cores, and furthermore, that for $n/r = n'/r'$ there exists a homomorphism $K_{n:r}\\to K_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.10002","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"}