On 3-cutwidth critical graphs

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 five specified elements.