Abstract The minimum leaf number of a connected non-hamiltonian graph G is the number of leaves of a spanning tree of G with the fewest leaves among all spanning trees of G . Based on this quantity, Wiener introduced leaf-stable and leaf-critical graphs, concepts which generalise hypotraceability and hypohamiltonicity. In this article, we present new methods to construct leaf-stable and leaf-critical graphs and study their properties. Furthermore, we improve several bounds related to these families of graphs. These extend previous results of Horton, Thomassen, and Wiener.

中文翻译：

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关于最小叶生成树和临界性概念

摘要 连通非哈密顿图G的最小叶子数是G的所有生成树中叶子最少的G的生成树的叶子数。基于这个数量，维纳引入了叶稳定图和叶临界图，这些概念概括了低追踪性和低浓度。在本文中，我们提出了构建叶稳定图和叶临界图的新方法并研究它们的特性。此外，我们改进了与这些图族相关的几个边界。这些扩展了 Horton、Thomassen 和 Wiener 之前的结果。