Connected even factors in k-tree

Abstract

A connected even [2,2s]{[}2,2s]-factor of a graph G is a connected factor with all vertices of degree i(i=2,4,…,2s)i(i=2,4,\ldots ,2s), where s≥1s\ge 1 is an integer. In this paper, we show that a k+1s+2\tfrac{k+1}{s+2}-tough k-tree has a connected even [2,2s]{[}2,2s]-factor and thereby generalize the result that a k+13\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].

Keywords

• t-tough graph
• k-tree
• even connected factor [2, 2s]-factor
• 05c45