The problem of determining whether a given k-colored graph is a subgra
ph of a properly colored interval graph has an application in DNA phys
ical mapping. In this paper, we study the problem for the case that th
e number of colors k is fixed. For k = 2, we give a simple linear time
algorithm, for k = 3, we give an O(n(2)) algorithm for biconnected gr
aphs with n vertices, and for k = 4, we show that the problem is NP-co
mplete.