{"paper":{"title":"Changing of the domination number of a graph: edge multisubdivision and edge removal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladimir Samodivkin","submitted_at":"2015-02-22T16:37:01Z","abstract_excerpt":"For a graphical property $\\mathcal{P}$ and a graph $G$, a subset $S$ of vertices of $G$ is a $\\mathcal{P}$-set if the subgraph induced by $S$ has the property $\\mathcal{P}$. The domination number with respect to the property $\\mathcal{P}$, denoted by $\\gamma_{\\mathcal{P}} (G)$, is the minimum cardinality of a dominating $\\mathcal{P}$-set. We define the domination multisubdivision number with respect to $\\mathcal{P}$,denoted by $msd_{\\mathcal{P}}(G)$, as a minimum positive integer $k$ such that there exists an edge which must be subdivided $k$ times to change $\\gamma_\\mathcal{P} (G)$. In this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06245","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"}