Weighted book thickness can require strictly more pages than classical book thickness, already for a 10-vertex planar graph and for a 2-tree, but equals the 2-page value for all pathwidth-2 graphs.
A short proof of the NP -completeness of minimum sum interval coloring
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Weighted Book Thickness
Weighted book thickness can require strictly more pages than classical book thickness, already for a 10-vertex planar graph and for a 2-tree, but equals the 2-page value for all pathwidth-2 graphs.