Abstract A graph G is t*-connected if there exist t internally disjoint (u, v)-paths, between any two vertices u and v, whose union spans G. In this sense, t*-connectedness is a natural extension of hamiltonicity. In this paper, we provide a sufficient condition for graphs to be t*-connected by generalizing a classic result given by Chavatal [7]. Furthermore, as byproducts, we extend some known results concerning fault tolerant hamiltonicity and minimum cardinality of edges. We also establish analogous results for balanced bipartite graphs.

中文翻译：

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图跨越连通的充分条件

摘要 如果在任意两个顶点 u 和 v 之间存在 t 条内部不相交的 (u, v)-路径，则图 G 是 t*-连通的，它们的并集跨越 G。从这个意义上说，t*-连通性是半调性的自然延伸. 在本文中，我们通过推广 Chavatal [7] 给出的经典结果，为图为 t*-连通提供了充分条件。此外，作为副产品，我们扩展了一些关于容错半调性和边的最小基数的已知结果。我们还为平衡二分图建立了类似的结果。