{"paper":{"title":"Graphs with $C_3_-free vertices are not universal fixers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Magdalena Lema\\'nska, Monika Rosicka, Rita Zuazua","submitted_at":"2013-09-03T08:04:42Z","abstract_excerpt":"A non-isolated vertex $x\\in V(G)$ is called $C_{3}$-free if $x$ belongs to no triangle of $G$. In \\cite{BMW} Burger, Mynhardt and Weakley introduced the idea of universal fixers. Let $G=(V,E)$ be a graph with $n$ vertices and $G'$ a copy of $G$. For a bijective function $\\pi:V(G)\\mapsto V (G')$, we define the prism $\\pi G$ of $G$ as follows: $V(\\pi G)=V(G)\\cup V(G')$ and $E(\\pi G)=E(G)\\cup E(G')\\cup M_{\\pi}$, where $M_{\\pi}=\\{u\\pi (u): u\\in V(G)\\}$. Let $\\gamma(G)$ be the domination number of $G$. If $\\gamma(\\pi G)=\\gamma(G)$ for any bijective function $\\pi$, then $G$ is called a universal fix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0603","kind":"arxiv","version":2},"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"}