标题： 三阶和n-1阶的圈在Bang-Jensen-Gutin-Li类型条件下的有向图中 显示英文标题

标题： Cycles of lengths 3 and n-1 in digraphs under a Bang-Jensen-Gutin-Li type conditon

摘要： Bang-Jensen-Gutin-Li 类型条件是针对有向图哈密尔顿性的条件，这些条件对具有共同内邻点或外邻点的非相邻顶点施加了度数限制。它们可以被视为无向图中 Fan 类型条件的扩展，同时也是局部（内-外）半完全有向图的推广。自 1996 年首次出现以来，各种 Bang-Jensen-Gutin-Li 类型的哈密尔顿性条件相继提出。本文建立了一种 Bang-Jensen-Gutin-Li 类型的条件，该条件不仅意味着存在哈密尔顿回路，还意味着存在 3-圈和 (n-1)-圈，并且具有特征明确的例外图。我们推测这一条件意味着存在任意长度的圈。 显示英文摘要

摘要： Bang-Jensen-Gutin-Li type conditions are the conditions for hamiltonicity of digraphs which impose degree restrictions on nonadjacent vertices which have a common in-neighbor or a common out-neighbor. They can be viewed as an extension of Fan type conditions in undirected graphs, as well as generalization of locally (in-, out-)semicomplete digraphs. Since their first appearance in 1996, various Bang-Jensen-Gutin-Li type conditions for hamitonicity have come forth. In this paper we establish a condition of Bang-Jensen-Gutin-Li type which implies not only a hamiltonian cycle but also a 3-cycle and an (n-1)-cycle, with well-characterized exceptional graphs. We conjecture that this condition implies the existence of cycle of every length.