Notion of flows and flow-colouring duality in graph theory

The main source used in the preparation of this study is Diestel's (2017) "Graph Theory" book. This thesis mainly consists of studying the sixth chapter of the aforementioned book to understand and explain the "notion of flows and flow-colouring duality in graph theory", as can be understood from the title of the thesis. 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: This study started with a short introduction about the importance of the thesis topic and its meaning in life. In the second chapter, basic definitions and theorems of graph theory, which are the prerequisites for understanding the main subject, are discussed by using the first part of the aforementioned book. In the first section of the third chapter, basic definitions about circulations are given; in the second section, the flows in the networks are studied and the "max-flow min-cut" theorem is proved. In the third section, group-valued flows are introduced; in the fourth section, k-flows are studied for k=2, 3, and 4 values. The next section explores the surprising connection between flow and colouring; in the last section, Tutte's flow conjectures are discussed. In the fourth 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 sixth chapter of the mentioned book.