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When the vertices of an n-vertex graph G are numbered by the integers 1 through n, the length of an edge is the difference between the numbers on its endpoints. Two edges overlap if the larger of their lower numbers is less than the smaller of their upper numbers. The bandwidth of G is the minimum, over all numberings, of the maximum length of an edge. The cutwidth of G is the minimum, over all numberings,...
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...
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