The book A History of Mathematics: An Introduction
by Victor J. Katz says:
"...probably the most famous mathematical technique coming
from China is the technique long known as the Chinese
remainder theorem. This result was so named after a
description of some congruence problems appeared in one
of the first reports in the West on Chinese mathematics,
articles by Alexander Wylie published in 1852 in the
North China Herald, which were soon translated into both
German and French and republished in European journals..."
(page 222)
This seems to suggest that the name "Chinese Remainder Theorem"
was introduced soon after Wylie's 1852 article.
But the book Historical Perspectives on East Asian Science,
Technology, and Medicine, edited by Alan Kam-leung Chan,
Gregory K. Clancey and Hui-Chieh Loy says:
"A. Wylie introduced the solution of Sun Zi's remainder
problem (i.e. "Wu Bu Zhi Shu") and Da-Yan Shu to the
West in 1852, and L. Matthiessen pointed out the identity
of Qin Jiushao's solution with the rule given by C. F. Gauss
in his Disquisitiones Arithmeticae in 1874. Since then it
has been called the Chinese Remainder Theorem in Western
books on the history of mathematics."
This is ambiguous, as it is not clear whether the author
means that the name "Chinese Remainder Theorem" came into
use after 1852 or after 1874. But the phrasing does suggest
that the name came into use before 1929.
In 1881, Matthiessen published the following article:
L. Matthiessen. "Le problème des restes dans l'ouvrage
chinois Swang-King de Sum-Tzi et dans l'ouvrage Ta Sen
Lei Schu de Yihhing." Comptes rendus de l'Académie de
Paris, 92 :291-294, 1881.
But does the name "Chinese Remainder Theorem"
("le théorème chinois des restes") appear in this article?
There is an interaction between category theory and graph theory in
F.~W.~Lawvere. Qualitative distinctions between some toposes of generalized graphs. In {\em Categories in computer science and logic (Boulder, CO, 1987)/}, volume~92 of {\em Contemp. Math./}, 261--299. Amer. Math. Soc., Providence, RI (1989).
which we have exploited in
R. Brown, I. Morris, J. Shrimpton and C.D. Wensley, `Graphs of Morphisms of Graphs', Electronic Journal of Combinatorics, A1 of Volume 15(1), 2008. 1-28.
But that is actually about possible categories of graphs, which may be the opposite of the question you ask.
If you look at groupoid theory, then "underlying graphs" are fundamental, for example in defining free groupoids. See for example
Higgins, P.~J. Notes on categories and groupoids, Mathematical Studies, Volume~32. Van Nostrand Reinhold Co. London (1971); Reprints in Theory and Applications of Categories, No. 7 (2005) pp 1-195.
Groupoids are kind of "group theory + graphs".
Best Answer
Dear Jérôme, I doubt that Grothendieck ever said that.
However, in an analogous vein, Jean Leray, a brilliant French mathematician, was taken prisoner by the Germans in 1940 and sent to Oflag XVIIA ("Offizierslager", officers' prison camp) in Edelsbach (Austria), where he remained for five years till the end of WW2.
He managed to hide from his captors that he was an expert in fluid dynamics and mechanics, lest they would force him to contribute to their war effort (submarines, planes). Instead, he organized a course, attended by his fellow prisoners, on the foundations of Algebraic Topology, a harmless subject for applications in his eyes. It is in these courses that he introduced sheaves, cohomology of sheaves and spectral sequences.
His strategy worked out fine since these discoveries didn't play any role in the construction of weapons by the German enemy, who never cared about Leray's courses and findings. On the other hand, these theoretical tools have had a non entirely negligible role in pure mathematics since.