Basics I: Graphs

Abstract

The birth of graph theory dates back to Leonhard Euler (1707–1783), who studied the problem whether one could stroll around Königsberg and thereby crossing each bridge across the Pregel exactly once. Abstracting this problem into a mathematical setting leads to the notion of a graph. While in the 18th and 19th century graph theory played only a marginal role within mathematics, in the 20th century the importance of graph theory dramatically increased, last but not least due to the interplay with computer science. In this chapter we can therefore give only a first glance at this important part of modern mathematics.