Let and be any two distinct nodes of an undirected graph , which is -connected. For , a -container of a -connected graph is a set of -disjoint paths joining and . A -container of is a -container if it contains all the nodes of . A graph is -connected if there exists a -container between any two distinct nodes. A bipartite graph is -laceable if there exists a -container between any two nodes from different parts of . Let and be two disjoint graphs with . Let , and is a bijection. Let . The set of -dimensional hypercube-like graph is defined recursively as (a) , complete graph with two nodes, and (b) if and are in , then is in . Let and is bipartite and . In this paper, we show that every graph in is -laceable for every , . It is shown that a constructed -graph can not be -connected. In addition, we show that every graph in is -connected for every , .