Claw-free graphs — A survey Original Research Article

In this paper we summarize known results on claw-free graphs. The paper is subdivided into the following chapters and sections: 1. 1. Introduction 2. 2. Paths, cycles, hamiltonicity 2.1. (a) Preliminaries 2.2. (b) Degree and neighborhood conditions 2.3. (c) Local connectivity conditions 2.4. (d) Further forbidden subgraphs 2.5. (e) Invariants 2.6. (f) Squares 2.7. (g) Regular graphs 2.8. (h) Other hamiltonicity related results and generalizations 2.9. 3. Matchings and factors 2.10. 4. Independence, domination, other invariants and extremal problems 2.11. 5. Algorithmic aspects 2.12. 6. Miscellaneous 2.13. 7. Appendix — List of all 2-connected nonhamiltonian claw-free graphs on n ⩽ 12 vertices.