We determine completely which graphical sequences d₁ d₂ ⋯ dₚ with d₁ - dₚ = 1 are planar graphical, and with a small number of exceptions determine the same result when d₁ - dₚ = 2. We also give simple necessary conditions (in the form of upper bounds on ∑i = 1ᵏ di) for a graphical sequence to be planar graphical. These conditions imply all known conditions of similar type, and often improve them.
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Schmeichel et al. (1977) studied this question.
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