Running summarizing tools on a new article

Abstract: In this first chapter, we provide a gentle introduction to several basic but fundamental concepts in graph theory, such as paths, trees, connected components, independent sets and the chromatic number, illustrating each definition with some simple but important properties that will be used in later chapters. We also take the opportunity to introduce (in a very simple setting) the probabilistic method, which plays a central role in the book. In the second half of the chapter we introduce the reader to planar graphs, and provide a brief taste of some simple results from the areas of extremal graph theory and Ramsey theory, which are the central topics of Chapters 2 and 4, respectively.