In this paper, we define the notion of -consistency and -graph associated with general n-ary constraint satisfaction problems and present an alternative sufficient condition for backtrack-free search; that is, if the hypergraph associated with a general CSP has a tree-structured -graph, then enforcing -consistency enables the CSP to be solved by search without backtracking. We then show that the subclass of tractable CSPs identified with the new condition contains the subclass of tractable CSPs identified previously.