Geodesic
Edge-maximal graphs with cutwidth at most three
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 635-657

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The cutwidth minimization problem consists of finding an arrangement of the vertices of a graph G on a line P_n with n=|V(G)| vertices, in such a way that the maximum number of edges between each pair of consecutive vertices is minimized. A graph G with cutwidth k (k≥ 1) is edge-maximal if c(G+uv) gt;k for any uv∈{uv: u,v∈ V(G) and uv∉ E(G)}. In this paper, we provide a complete insight to structural properties of edge-maximal graphs with cutwidth at most 3.
Keywords: combinatorics, graph labeling, cutwidth, edge-maximal graph 
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Zhang, Zhen-Kun. Edge-maximal graphs with cutwidth at most three. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 635-657. http://geodesic.mathdoc.fr/item/DMGT_2023_43_3_a3/