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Ικανές συνθήκες για την ύπαρξη υπογραφημάτων με καθορισμένη δομή σε ειδικές κατηγορίες γραφημάτων
Φουρτουνέλλη, Όλγα; Athens School of Economics and Business, Department of Informatics; Κατερίνης, Παναγιώτης
The purpose of this thesis is to establish sufficient conditions for the existence of factors with prescribed properties in special classes of graphs; mainly in terms of the graph invariants of connectivity and minimum degree. The thesis starts by examining the relation between the minimum degree of a claw-free graph and the existence of a 2-factor which includes or excludes a given pair of edges. Chapter 2 examines the relation between the edge-connectivity of a regular graph and the existence of a 2-factor which again includes and excludes respectively two given sets of edges. Finally in chapter 3, we obtain a sufficient condition for the square of a graph G to have a k-factor. This sufficient condition is expressed in terms of the minimum degree of G and generalizes an already known result.