Abstract A strongly edge-colored graph is an edge-colored graph in which every path of length 3 is rainbow or, equivalently, every monochromatic subgraph is an induced matching. In this paper, we show that every strongly edge-colored graph with n vertices and minimum degree δ ≥ 2 n ∕ 3 is rainbow vertex-pancyclic. This extends a recent result given by Cheng et al., that is, every strongly edge-colored graph with n vertices and minimum degree δ ≥ 2 n ∕ 3 is rainbow Hamiltonian.

中文翻译：

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强边彩色图的彩虹顶点泛循环性

摘要 强边着色图是边着色图，其中每条长度为 3 的路径都是彩虹，或者等价地，每个单色子图都是诱导匹配。在本文中，我们证明了每个具有 n 个顶点且最小度数 δ ≥ 2 n ∕ 3 的强边着色图都是彩虹顶点泛环图。这扩展了 Cheng 等人最近给出的结果，即每个具有 n 个顶点且最小度数 δ ≥ 2 n ∕ 3 的强边着色图都是彩虹哈密顿量。