Abstract
A special class of interval graphs is defined and characterized, and an algorithm is given for their construction. These graphs are motivated by an important representation of DNA called restriction maps by molecular biologists. Circular restriction maps are easily included.
Similar content being viewed by others
Literature
Benzer, S. 1959. “On the topology of genetic fine structure.”Proc. natn. Acad. Sci. U.S.A. 45, 1607–1620.
Booth, K. S. and G. S. Leuker. 1976. “Testing for the consecutive ones property, interval graphs, and graph planarity using PO algorithms.”J. Comput. Syst. Sci. 13, 335–379.
Danna, K. J., G. H. Sack and D. Nathans. 1973. “Studies of Simian Virus 40 DNA. VII. A cleavage map of the SV40 genome.”J. molec. Biol. 78, 363–376.
Fitch, W. M., T. F. Smith, and W. W. Ralph. 1983. “Mapping the order of DNA restriction fragments.”Gene 22, 19–29.
Fulkerson, D. R. and O. A. Gross. 1964. “Incidence matrices with the consecutive 1s property.”Bull. Am. math. Soc. 70, 681–684.
Gilmore, P. C. and A. J. Hoffman. 1964. “A characterization of comparability graphs and of interval graphs.”Can. J. Math. 16, 539–548.
Golumbic, M. C. 1980.Algorithmic Graph Theory and Perfect Graphs. New York: Academic Press.
Jungck, J. R., G. Dick and A. G. Dick. 1982. “Computer-assisted sequencing, interval graphs, and molecular evolution.”Bio-Syst. 15, 259–273.
Lekkerkerker, C. G. and J. C. Boland. 1962. “Representation of a finite graph by a set of intervals on the real line.”Fund. Math. 51, 45–64.
Author information
Authors and Affiliations
Additional information
Supported by a grant from the System Development Foundation.
Supported by an NSF grant and through a grant from the System Development Foundation.
Rights and permissions
About this article
Cite this article
Waterman, M.S., Griggs, J.R. Interval graphs and maps of DNA. Bltn Mathcal Biology 48, 189–195 (1986). https://doi.org/10.1007/BF02460022
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460022