{"paper":{"title":"Graphs with conflict-free connection number two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Chang, Ingo Schiermeyer, Stanislav Jendrol', Trung Duy Doan, Xueliang Li, Zhong Huang","submitted_at":"2017-07-06T04:47:26Z","abstract_excerpt":"An edge-colored graph $G$ is \\emph{conflict-free connected} if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The \\emph{conflict-free connection number} of a connected graph $G$, denoted by $cfc(G)$, is the smallest number of colors needed in order to make $G$ conflict-free connected. For a graph $G,$ let $C(G)$ be the subgraph of $G$ induced by its set of cut-edges. In this paper, we first show that, if $G$ is a connected non-complete graph $G$ of order $n\\geq 9$ with $C(G)$ being a linear forest and with the minimum degree %$\\delta(G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01634","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"}