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The cutwidth of a graph G is the minimum congestion (the number of overlap edges) when G is embedded into a path. The cutwidth problem has been motivated from both applied and theoretical points of view. The characterization of forbidden subgraphs or critical graphs is always interesting in the study of a graph-theoretic parameter. In this paper we characterize the set of 3-cutwidth critical graphs by ÿve speciÿed elements.doi:10.1016/j.disc.2003.06.012 fatcat:6btteq7ujzfa3bvghi3xikjzpm