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: Characterizations and recognition of circular-arc graphs and subclasses: A survey 
Chapter Title:  Theorem 13 ([65] 
1. Abstract of Cited Paper (BIB001):  We give a forbidden substructure characterization of set families that have the consecutive-ones property, and a linear time algorithm to find the forbidden substructure if a set family does not have the property. The forbidden substructure has size O(n), where n is the size of the domain. The PQ tree is a well-known data structure for representing all consecutive-ones orderings. We show that it is given by a substitution decomposition of arbitrary set families that has not been described previously. This observation gives a generalization of the PQ tree to arbitrary set families, and we give a linear-time algorithm to compute it. 
2. Abstract of Cited Paper (BIB002):  We give two new algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time.

Literature Review:
): Let G be a co-bipartite graph. Then G is a PCA graph if and only if G is a permutation graph. The algorithm  then recognizes co-bipartite PCA graphs G by deciding if G is a permutation graph. Since we know that G is bipartite, a simpler linear time algorithm can be applied to decide if G is indeed a permutation graph. Consequently, the overall complexity of this algorithm is O(n + m). Note that Theorems 8 and 13 imply that the classes of proper interval bigraphs and bipartite permutation graphs are equivalent. Moreover, these classes are also equivalent to bipartite asteroid-free graphs  . More recently, Kaplan and Nussbaum BIB003 described another linear time recognition algorithm for PCA graphs, aiming at producing certificates. Such algorithm again considers two cases. When G is not co-bipartite, Kaplan and Nussbaum also apply Tucker's characterization (Theorem 6). In this case, for obtaining a certificate for the circular consecutive 1's property, they employ the algorithm by McConnell BIB002 (see also BIB001 ). The algorithm BIB002 produces a certificate for the augmented adjacency matrix not having the consecutive 1's property. However, in this situation we need a relation between the consecutive 1's property and the circular consecutive 1's property. The following theorem provides this relation. BIB003 then exhibits a convenient forbidden structure.