Ebook: Examples and Counterexamples in Graph Theory

North-Holland, 1978. - 270 pages.It is a real pleasure, indeed an honor, for me to have been invited by Mike Capobianco and John Molluzzo to write an introduction to this imaginative and valuable addition to graph theory. Let me therefore present a few of my thoughts on the current status of graph theory and how their work contributes to the field.Graphs have come a long way since 1736 when Leonhard Euler applied a graph-theoretic argument to solve the problem of the seven Konigsberg bridges. At first, interest in and results involving graphs came slowly. Two centuries passed before the first book exclusively devoted to graphs was written. Its author, Denes Konig, referred to his 1936 publication as "The Theory of Finite and Infinite Graphs" (translated from the German). The results on graphs obtained during the time between Konigberg and Konig's book were indeed developing into a theory. In the past several years a number of changes have taken place in graph theory. The applicability of graphs and graph theory to a wide range of areas both within and outside mathematics has given added stature to this youthful subject. It is clear that the full potential and usefulness of graph theory is only beginning to be realized.