Notions of matching, covering and packing in graph theory

The main source used in the preparation of this thesis is Diestel's (2017) "Graph Theory" book. Essentially, what we do is to translate the second chapter of the mentioned book into Turkish to understand and explain the concepts of "notions of matching, covering and packing in graph theory", as can be understood from the title of the thesis. But of course, no literal translation was made, 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, the basic definitions and theorems of graph theory, which are prerequisites for understanding this study, are given by adding the necessary part of the first chapter of the aforementioned book to the thesis. In addition to these, the articles listed in the references were also consulted. To summarize: In the first chapter, after the basic definitions, necessary definitions and theorems related to roads and loops, connectedness, trees and forests, and bipartite graphs are covered. In the first section of the second part, König (1931) and Hall's (1935) theorems for bipartite graphs are proved; in the second section, Tutte's (1947) theorem related to matching in general graphs is proved. In the third section, the theorem of Erdös and Posa (1965) is expressed. In the fourth section, packing and covering concepts are discussed in terms of edges, and tree-packing (Nash-Williams 1961, Tutte 1961) and tree-covering (Nash-Williams 1964) theorems are proved as a result of the packing-covering theorem (Bowler and Carmesin 2015). In the fifth and final section, Dilworth's (1950) duality theorem for partial orders is proved as a result of Gallai and Milligram's (1960) path cover theorem for directed graphs. In the third chapter of the thesis, before the conclusions and recommendation chapter, a brief literature review on the subject of the thesis is presented by using the notes section of the second chapter of the mentioned book.