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Theory of Finite and Infinite Graphs (Paperback, Softcover reprint of the original 1st ed. 1990)
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Theory of Finite and Infinite Graphs (Paperback, Softcover reprint of the original 1st ed. 1990)
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To most graph theorists there are two outstanding landmarks in the
history of their subject. One is Euler's solution of the Konigsberg
Bridges Problem, dated 1736, and the other is the appearance of
Denes Konig's textbook in 1936. "From Konigsberg to Konig's book"
sings the poetess, "So runs the graphic tale ..." [10]. There were
earlier books that took note of graph theory. Veb- len's Analysis
Situs, published in 1931, is about general combinato- rial
topology. But its first two chapters, on "Linear graphs" and
"Two-Dimensional Complexes", are almost exclusively concerned with
the territory still explored by graph theorists. Rouse Ball's
Mathematical Recreations and Essays told, usually without proofs,
of the major graph-theoretical advances ofthe nineteenth century,
of the Five Colour Theorem, of Petersen's Theorem on I-factors, and
of Cayley's enumerations of trees. It was Rouse Ball's book that
kindled my own graph-theoretical enthusiasm. The graph-theoretical
papers of Hassler Whitney, published in 1931-1933, would have made
an excellent textbook in English had they been collected and
published as such. But the honour of presenting Graph Theory to the
mathe- matical world as a subject in its own right, with its own
textbook, belongs to Denes Konig. Low was the prestige of Graph
Theory in the Dirty Thirties. It is still remembered, with
resentment now shading into amuse- ment, how one mathematician
scorned it as "The slums of Topol- ogy".
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