{"paper":{"title":"An improved bound in Vizing's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shira Zerbib","submitted_at":"2017-06-12T15:21:30Z","abstract_excerpt":"A well-known conjecture of Vizing is that $\\gamma(G \\square H) \\ge \\gamma(G)\\gamma(H)$ for any pair of graphs $G, H$, where $\\gamma$ is the domination number and $G \\square H$ is the Cartesian product of $G$ and $H$. Suen and Tarr, improving a result of Clark and Suen, showed $\\gamma(G \\square H) \\ge \\frac{1}{2}\\gamma(G)\\gamma(H) + \\frac{1}{2}\\min(\\gamma(G),\\gamma(H))$. We further improve their result by showing $\\gamma(G \\square H) \\ge \\frac{1}{2}\\gamma(G)\\gamma(H) + \\frac{1}{2}\\max(\\gamma(G),\\gamma(H)).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03682","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"}