A discussion of autosegmental phonology (AP), a theory of phonological representation that uses graphs rather than strings as the central data structure, considers its principal constraint, the "No Crossing Constraint" (NCC). The NCC is the statement that in a well-formed autosegmental diagram, lines of association may not cross. After an introductory section, the syntax and semantics of autosegmental representations are considered, and a few important basic definitions and principles of graph theory are introduced. In section 3, two claims are examined, including: the claim that the NCC restricts the class of representations in planar and non-planar AP; and the belief of some proponents of three-dimensional AP that the necessity of non-planar representations has been demonstrated. Finally, some data exemplifying a number of interacting harmonies in Guyanese English that are amenable only to non-planar representation are presented. It is concluded that the NCC is invalid because it either incorrectly restricts the class of phonological graphs to planar graphs or else carries no force. (MSE)