Ramsey theory for graphs and essentials of graph colouring

The main source used in the preparation of this study is Diestel's (2017) "Graph Theory" book. This thesis mainly consists of studying the ninth and fifth chapters of the aforementioned book to understand and explain the subjects of "Ramsey theory for graphs and essentials of graph colouring". But of course, no part of the mentioned book has been quoted exactly, a study has been put forward with our own words and our own sentences; and on the one hand, some very difficult or technical proofs were skipped, on the other hand, some parts of the book that were left to the reader were explained and the subject was presented more understandably. In addition to these, the articles listed in the references were also consulted. To summarize in outline: In the first section of the first chapter, the original theorem of Ramsey (1930) is proved and the related definitions and results are given; in the second section, definitions and results related to the equivalent of Ramsey numbers in graph theory are presented; in the third section, the expression of the induced Ramsey theorem is contented with; in the fourth and the last section, the relationship between Ramsey features and connectedness is examined. In the first section of the second chapter, the five colour theorem is proved; in the second and third sections, the basic definitions and theorems of vertex colouring and edge colouring are presented, respectively. In the third chapter of the thesis, before the conclusions and recommendation, a brief literature review on the subject of the thesis is presented by using the notes section of the ninth and fifth chapters of the mentioned book.