{"paper":{"title":"Vizing-type bounds for graphs with induced subgraph restrictions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elliot Krop, Gaspar Porta, Pritul Patel","submitted_at":"2017-05-14T11:51:46Z","abstract_excerpt":"For any graphs $G$ and $H$, we say that a bound is of Vizing-type if $\\gamma(G\\square H)\\geq c \\gamma(G)\\gamma(H)$ for some constant $c$. We show several bounds of Vizing-type for graphs $G$ with forbidden induced subgraphs. In particular, if $G$ is a triangle and $K_{1,r}$-free graph, then for any graph $H$, $\\gamma(G\\square H)\\geq \\frac{r}{2r-1}\\gamma(G)\\gamma(H)$. If $G$ is a $K_r$ and $P_5$-free graph for some integer $r\\geq 2$, then for any graph $H$, $\\gamma(G\\square H)\\geq \\frac{r-1}{2r-3}\\gamma(G)\\gamma(H)$. We do this by bounding the power of $G$, $\\pi(G)$. We show that if $G$ is claw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04954","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"}