{"paper":{"title":"Some extremal results on the colorful monochromatic vertex-connectivity of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Di Wu, Qingqiong Cai, Xueliang Li","submitted_at":"2015-03-31T07:44:46Z","abstract_excerpt":"A path in a vertex-colored graph is called a \\emph{vertex-monochromatic path} if its internal vertices have the same color. A vertex-coloring of a graph is a \\emph{monochromatic vertex-connection coloring} (\\emph{MVC-coloring} for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph $G$, the \\emph{monochromatic vertex-connection number}, denoted by $mvc(G)$, is defined to be the maximum number of colors used in an \\emph{MVC-coloring} of $G$. These concepts of vertex-version are natural generalizations of the colorful monochromatic connect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08941","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"}