Claw-free graphs. V. Global structure
This is the fifth of a series of \(5\) papers by the same authors with the objective of describing the structure of claw-free graphs. The four preceding papers are: [``Claw-free graphs I. Orientable prismatic graph, Claw-free graphs II. Non-orientable prismatic graphs, and Claw-free graphs III. Circular interval graphs and Claw-free graph IV. Decomposition Theorem'', all of which appeared in: J. Comb. Theory, Ser. B 97, No.\,6, 867--903 (2007; Zbl 1128.05031), 98, No.\,2, 249--290 (2008; Zbl 1137.05040), 98, No.\,4, 812--834 (2008; Zbl 1158.05035), and 98, No.\,5, 839--938 (2008; Zbl 1152.05038)] respectively. The main result of the fourth paper was a decomposition theorem for claw-free graph built on the decompositions and characterizations of the three previous papers. As the title indicates this paper provides the global structure of claw free graphs. The objective is to describe how to start with basic classes of claw-free graphs and some constructions that build larger claw-free graph from graphs in these basic classes to obtain general claw-free graphs. Thus, in some sense, this reverses the process of the fourth paper. The papers clearly build on the previous papers, so having all the preceding papers is useful in reading the final two papers.
scientific article; zbMATH DE number 5379223