Abstract
The purpose of this introduction is to familiarise the reader with the basic concepts and results of graph theory. The chapter inevitably contains a large number of definitions and in order to prevent the reader growing weary we prove simple results as soon as possible. The reader is not expected to have complete mastery of Chapter I before sampling the rest of the book, indeed, he is encouraged to skip ahead since most of the terminology is self-explanatory. We should add at this stage that the terminology of graph theory is far from being standard, though that used in this book is well accepted.
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Notes
Theorem 14 is in K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930) 271–283
for a simpler proof see G. A. Dirac and S. Schuster, A theorem of Kuratowski, Indag. Math. 16 (1954) 343–348.
The theorem of S. A. Amitsur and J. Levitzki (Theorem 14) is in Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950) 449–463
the proof given in the text is based on R. G. Swan, An application of graph theory to algebra, Proc. Amer. Math. Soc. 14 (1963) 367–373.
R. G. Swan, Correction to “An application of graph theory to algebra,” Proc. Amer. Math. Soc. 21 (1969) 379–380.
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Bollobás, B. (1979). Fundamentals. In: Graph Theory. Graduate Texts in Mathematics, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9967-7_1
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