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We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which xi=yi+1=1 or vice versa. We give relatively close bounds on the maximum number of binary sequences of length n any pair of which has a skewincidence. A systematic study of these problems helps to understand the mathematical difficulties to solve zero-error problems in information theory.