Date of Award
Doctor of Philosophy
This dissertation concerns two types of problems in Extremal Graph Theory. The first type is on the edge spectrum of saturated graphs, while the second one is related to a combinatorial game.In the first chapter we give an overview of the structure of the dissertation, introduce some notation and definitions, and state some results that are repeatedly used for reference.In Chapter 2, we analyze the edge spectrum of star-saturated graphs. In particular, we show that there are star-saturated graphs for any number between the saturation number and the extremal number.Chapter 3 is dedicated to a problem similar to that in Chapter 2. Namely, we study the edge spectrum of path-saturated graphs and show that it includes all integers from the saturation number to slightly below the extremal number. Moreover, we analyze the structure of large path-saturated graphs that have edge counts close to the extremal number in order to show that there are some gaps in the edge spectrum of path-saturated graphs near the extremal number.We continue with path-saturated graphs in Chapter 4, and determine the size of the second largest path saturated graph.Chapter 5 deals with a combinatorial game. Namely, we study the H-Saturation Game when H is a path.
dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Dogan, Ali, "On Saturated Graphs and Combinatorial Games" (2016). Electronic Theses and Dissertations. 1360.