According to Golumbic , Hajös proposed the following problem in 1957 (translation by Golumbic):
Given a finite number of intervals on a straight line, a graph associated with this set of intervals can be constructed in the following manner: each interval corresponds to a vertex of the graph, and two vertices are connected by an edge if and only if the corresponding intervals overlap at least partially. The question is whether a given graph is isomorphic to one of the graphs just characterized (Hajös [1957, p. 65, translated by M.C.G.]).
Golumbic also discusses how interval graphs were related to a question in biology made by Benzer  in 1959.
 Golumbic, Martin Charles. Algorithmic graph theory and perfect graphs. Vol. 57. Elsevier, 2004.
 Benzer, Seymour. "On the topology of the genetic fine structure." Proceedings of the National Academy of Sciences of the United States of America 45.11 (1959): 1607.