Turan problems in extremal graph theory and flexibility
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In this work we will study two distinct areas of graph theory: generalized Turan problems and graph flexibility. In the first chapter, we will provide some basic definitions and motivation. Chapters 2 and 3 contain two submitted papers showing that two graphs, the cycle on five vertices and the path on four vertices, are maximized by the Turan graph when forbidding sufficiently large cliques. In chapter 4, we present new results on graph flexibility and weak flexibility for planar graphs.