Claw-free graphs. V. Global structure
type: Item
instance of: scholarly article
title: Claw-free graphs. V. Global structure
zbMATH Open document ID: 1196.05043
author: Maria Chudnovsky
author: Paul Seymour
published in: Journal of Combinatorial Theory. Series B
publication date: 2008-12-08T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C76
zbMATH DE Number: 5379223
zbMATH Keywords: claw-free graphs
zbMATH Keywords: induced subgraph
zbMATH Keywords: line graphs
reviewed by: Ralph Faudree
MaRDI profile type: Publication
full work available at URL: j.jctb.2008.03.002
OpenAlex ID: W1965412489
cites work: Claw-free graphs. I: Orientable prismatic graphs
cites work: Claw-free graphs. II: Non-orientable prismatic graphs
cites work: Claw-free graphs. III: Circular interval graphs
cites work: Claw-free graphs. IV: Decomposition theorem
DOI: 10.1016/J.JCTB.2008.03.002
description: scientific article; zbMATH DE number 5379223