You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A Survey of the Algorithmic Properties of Simplicial, Upper Bound and Middle Graphs 
Chapter Title:  Simple Maximum Cut 
1. Abstract of Cited Paper (BIB001):  The complexity of the SIMPLE MAX CUT problem is investigated for several special classes of graphs. It is shown that this problem is NP-complete when restricted to one of the following classes: chordal graphs, undirected path graphs, split graphs, tripartite graphs, and graphs that are the complement of a bipartite graph. The problem can be solved in polynomial time, when restricted to graphs with bounded treewidth, or cographs. We also give large classes of graphs that can be seen as generalizations of classes of graphs with bounded treewidth and of the class of cographs, and allow polynomial time algorithms for the SIMPLE MAX CUT problem.

Literature Review:
For a graph G = (V, E), the simple maximum cut problem is to partition the vertex set into two sets so as to maximize the number of edges of G with one end in each set. For some time this problem has been known to be NP-complete for general graphs  , but for line graphs time O(n+e) is sufficient BIB001 . Just recently the problem has been shown to be NP-complete for split graphs BIB002 , and hence for simplicial graphs. The time complexities of this problem for upper bound graphs and for representative graphs of hereditary hypergraphs remain open problems.