부산대학교 도서관

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].