Abstract A connected even [ 2 , 2 s ] {[}2,2s] -factor of a graph G is a connected factor with all vertices of degree i ( i = 2 , 4 , … , 2 s ) i(i=2,4,\ldots ,2s) , where s ≥ 1 s\ge 1 is an integer. In this paper, we show that a k + 1 s + 2 \tfrac{k+1}{s+2} -tough k-tree has a connected even [ 2 , 2 s ] {[}2,2s] -factor and thereby generalize the result that a k + 1 3 \tfrac{k+1}{3} -tough k-tree is Hamiltonian in [Hajo Broersma, Liming Xiong, and Kiyoshi Yoshimoto, Toughness and hamiltonicity in k-trees, Discrete Math. 307 (2007), 832–838].

中文翻译：

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k树中的连接偶数因子

摘要图 G 的连通偶数 [ 2 , 2 s ] {[}2,2s] -因子是具有度数为 i ( i = 2 , 4 , … , 2 s ) i(i=2) 的所有顶点的连通因子,4,\ldots ,2s) ，其中 s ≥ 1 s\ge 1 是一个整数。在本文中，我们证明 ak + 1 s + 2 \tfrac{k+1}{s+2} -tough k-tree 有一个连通偶数 [ 2 , 2 s ] {[}2,2s] -factor 和从而概括在 [Hajo Broersma, Liming Xiong, and Kiyoshi Yoshimoto, Toughness and hamiltonicity in k-trees, Discrete Math. 中 ak + 1 3 \tfrac{k+1}{3} -tough k-tree 是哈密顿量的结果。307 (2007), 832–838]。