Graph theory is a comparatively young mathematical discipline. It is often hard to construct graphs that satisfy certain properties purely combinatorially, i.e., by taking a set of vertices and saying which vertex is connected to which. Often such areas of classical mathematics as number theory, geometry, or algebra are used for this, and the methods from the related areas are used to prove the properties of the obtained graphs. The examples are numerous, and many of them can be found in books and comprehensive survey articles. See, for example, Alon [2]; Babai and Frankl [5]; Biggs [6]; Füredi and Simonovits [12]; Brouwer and Haemers [8], and Alon and Spencer [3]. Here we wish to mention just a few such applications. The probabilistic method was used to prove the existence of certain graphs in Ramsey theory, and explicit constructions for these graphs are still unknown (see [3]). Constructions and analysis of Ramanujan graphs are often based on algebra and number theory. Methods of linear algebra are fundamental for studies of expanders and graphs with high degree of symmetry (see [5] and [8]). Lovász's proof [20] of a conjecture on the chromatic number of Kneser graphs made use of algebraic topology.Can the direction be reversed, i.e., can graph theory be used to obtain results in some classical areas of mathematics? Sometimes it can, but the number of such instances is much smaller. See, for example, Swan's proof of the Amitsur-Levitzki theorem [24], or a counterexample to Borsuk's conjecture by Kahn and Kalai [14] and related work by Bondarenko [7]. Extremal graph theory was used in probability by Katona [15], and in geometry and potential theory by Turán [25], and Erdős, Meir, Sos, and Turán [11]. For some applications of graph theory to linear algebra, see Doob [10]. A number of applications of graph theory to pure mathematics are mentioned in Lovász, Pyber,
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