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Sep 8, 2020 at 6:29 comment added JimN without any structure in the graph paths or in the sets weights, essentially all paths woul have to be checked ... unless in a shortest path problem, where a path from s-t going through an intermediate u, it doesn't matter how s gets to u, just the value at u is important. But the unio nof all your sets along the way would be different for every s-to-u path, so essentially all paths would have to be considered.
Sep 8, 2020 at 6:24 comment added JimN I have not seen this problem studied before. Sets on vertices have been used in describing graph dimension or list-colouring or preference lists in stable matching problems, for example. In general, intersection graphs are graphs where each vertex is a set and an edge represents a non-empty intersection of the two vertices. Those sets are sometimes geometrical points, or intervals of real lines, or just discrete sets.
Sep 6, 2020 at 23:31 comment added Rodrigo de Azevedo Why not post at cstheory.stackexchange.com?
Sep 6, 2020 at 8:51 history asked Victor CC BY-SA 4.0