Title:

Graph theory in America 18761950

This narrative is a history of the contributions made to graph theory in the United States of
America by American mathematicians and others who supported the growth of scholarship
in that country, between the years 1876 and 1950.
The beginning of this period coincided with the opening of the first research university
in the United States of America, The Johns Hopkins University (although undergraduates
were also taught), providing the facilities and impetus for the development of new ideas.
The hiring, from England, of one of the foremost mathematicians of the time provided the
necessary motivation for research and development for a new generation of American
scholars. In addition, it was at this time that homegrown research mathematicians were
first coming to prominence.
At the beginning of the twentieth century European interest in graph theory, and to
some extent the fourcolour problem, began to wane. Over three decades, American
mathematicians took up this field of study  notably, Oswald Veblen, George Birkhoff,
Philip Franklin, and Hassler Whitney. It is necessary to stress that these four
mathematicians and all the other scholars mentioned in this history were not just graph
theorists but worked in many other disciplines. Indeed, they not only made significant
contributions to diverse fields but, in some cases, they created those fields themselves and
set the standards for others to follow. Moreover, whilst they made considerable
contributions to graph theory in general, two of them developed important ideas in
connection with the fourcolour problem. Grounded in a paper by Alfred Bray Kempe that
was notorious for its fallacious 'proof' of the fourcolour theorem, these ideas were the
concepts of an unavoidable set and a reducible configuration.
To place the story of these scholars within the history of mathematics, America, and
graph theory, brief accounts are presented of the early years of graph theory, the early years
of mathematics and graph theory in the USA, and the effects of the founding of the first
institute for postgraduate study in America. Additionally, information has been included on
other influences by such global events as the two world wars, the depression, the influx of
European scholars into the United States of America, mainly during the 1930s, and the
parallel development of graph theory in Europe.
Until the end of the nineteenth century, graph theory had been almost entirely the
prerogative of European mathematicians. Perhaps the first work in graph theory carried out
in America was by Charles Sanders Peirce, arguably America's greatest logician and
philosopher at the time. In the 1860s, he studied the fourcolour conjecture and claimed to
have written at least two papers on the subject during that decade, but unfortunately neither
of these has survived. William Edward Story entered the field in 1879, with unfortunate
consequences, but it was not until 1897 that an American mathematician presented a lecture
on the subject, albeit only to have the paper disappear. Paul Wernicke presented a lecture
on the fourcolour problem to the American Mathematician Society, but again the paper has
not survived. However, his 1904 paper has survived and added to the story of graph theory,
and particularly the fourcolour conjecture.
The year 1912 saw the real beginning of American graph theory with Veblen and
Birkhoff publishing major contributions to the subject. It was around this time that
European mathematicians appeared to lose interest in graph theory. In the period 1912 to
1950 much of the progress made in the subject was from America and by 1950 not only had
the United States of America become the foremost country for mathematics, it was the
leading centre for graph theory.
