Graf teorisinde Hamilton çevrimleri ve derece dizileri

The main source used in the preparation of this study is Diestel's (2017) "Graph Theory" book. This thesis mainly consists of the tenth chapter of the aforementioned book to understand and explain the subjects of "Hamilton cycles and degree sequences in graph theory". 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 chapter, basic definitions and theorems of graph theory, which are the prerequisites for understanding the main subject, are covered by using the first chapter of the aforementioned book. In the first section of the second chapter, some sufficient conditions that guarantee the existence of a Hamiltonian cycle in a graph are examined, and theorems of Dirac (1952), and Asratian and Khachatrian (1990) are proved; in the second section, Chvatal (1972) theorem, which is a sufficient condition covering all previous results, is proved. In the third and last section, the theorems of Fleischner (1974), which states that the square of a 2-connected graph contains a Hamiltonian cycle, and Georgakopoulos (2009), which states that a similar situation is true for 2-connected locally finite graphs, are expressed, and. The chapter is completed with the Seymour (1974) conjecture, which is a comprehensive generalization of Dirac's (1952) theorem. 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 tenth chapter of the mentioned book.