A gauge theory with colour gauge group U(N) and quarks having a colour index running from one to N is considered in the limit N → ∞, g2N fixed. It is shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in 1/N is identical to that of the dual models, such that the number 1/N corresponds to the dual coupling constant. For hadrons N is probably equal to three. A mathematical framework is proposed to link these concepts of planar diagrams with the functional integrals of Gervais, Sakita and Mandelstam for the dual string.
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