Abstract: The space complexity of constructing cycle-like Traversal Sequences for（undirected） Connected Components （TSC） is studied.A new notion of log-space Cook reduction is put forward to analyze the relationships between TSC problem and the undirected connectivity and universal transversal sequence problems.It therefore implies that the TSC problem and traversal of undirected graph problem are equivalent and both solvable in log-space.The analyzing process produces a general approach of constructing TSC for any undirected graph.Finally，a specific but more efficient TSC construction algorithm for trees is also given.