I have graph creation problem.
Given a set of nodes of graph, and node constraints such as given every node's number of neighbors (degree). I am also provided with the total number of triangles in the graph. Given the above constraints ($n+1$), I have to generate a graph that satisfies all the constraints.
I know that given nodes' degrees, it is possible to construct using Havel–Hakimi algorithm a graph satisfying node degrees. But I am not sure how to fulfill the total triangle count constraint and if it makes the problem NP-hard.