The graph theory is of relatively recent origin. Some hints of the
graph theory can be found already in the 18th and 19th centuries, but the
first book devoted solely to the graph theory emerged as late as 1936.
The subject of the book were finite and infinite graphs and its author
was Hungarian mathematician D. König. An enourmously fast development of
this discipline started only after the Second World War. The contribution
of Czech and Slovak mathematician was very important. The aim of this work
is to map the development of the graph theory in the period from 1736 to
1963. The choice of dates is not arbitrary, for both years were important
milestones in the graph theory. In 1736 the first article on a topic relating
to graph theory was written by the Swiss mathematician L. Euler. In this
article Euler solved the wellknown problem of the Königsberg bridges. In
1963, the first international conference on the graph theory was held in
Smolenice-for the first time in Czechoslovakia.
Let us now introduce a short summary of this work.
In the introduction, we define basic terms needed for understanding the
core of the work. Our work consists of five chapters, which deal with the
historical development of the basic problems of the graph theory. Our sources
were primarily books N. L. Biggs, K. E. Lloyd and R. J. Wilson: Graph
theory 1736-1936. Oxford 1976 and D. König: Theorie der endlichen
und unendlichen Graphen. Leipzig 1936. The core lies in the analysis
of a number of original works, mainly from the years 1936-1970. The first
chapter maps the historical development of the concepts Eulerian graph
and Hamiltonian graph. It introduces the reader to the problem of Königsberg
bridges and the knight's tour in chess which belong to the oldest problems
of the graph theory. In the part devoted to Hamiltonian connected graphs
we look more closely at the work of Brno mathematician M. Sekanina. The
main subject of the second chapter is the spanning tree. The first part
maps the historical development of the concepts of tree, spanning tree,
and the fundamental set of circuits. Major attention is then devoted to
the problem of finding the minimum spanning tree. The first mathematicians
who tried to solve this problem were Czech mathematicians O. Borùvka and
V. Jarník. They were both successful: each of them found his own algorithm
in the 1920s. The third chapter deals with the coloration of graphs. The
development of the four-colour problem is described here in a detailed
way. We cover the period from the origins of the problem in 1852 until
1976, when this problem was solved. The four-colour problem had a great
influence on many other parts of the graph theory. Other subject dealt
with in this chapter are planar graphs. Factorization of graphs is the
subject of the fourth chapter. In the chapter, we follow especially the
questions of factorization of regular graphs in the works of. J. Petersen
and D. König. We also look in greater detail at the work of the Slovak
mathematician A. Kotzig and the research he carried out in the 1950s and
1960s. The fifth chapter is a brief overview of the oriented graphs. As
well as the other parts of the graph theory, the Czech and Slovak mathematicians
contributed largely to the development of the oriented graphs theory.
One of the major contributions of the work is also
a large bibliography. There are two appendices: the first is an anotated
list of roughly 300 early works of the graph theory dated 1736-1936, the
second is a similar list of roughly 70 works of Czech and Slovak authors
from the years 1926-1962.