Abstract
Two aspects of the Bennett model are of interest from a mathematical point of view. First there is the question whether Bennett's “ranking method” for predicting the order of chromosomes will always work. The answer depends on the number n of chromosomes: If n is odd, predictions (being not necessarily unique) are possible in most cases. Secondly there is Bennett's procedure for determining the arrangement of chromosomes. It is shown that the method of minimising the perimeter of the polygon obtained by connecting the centromeres is only applicable if the positions of the n centromeres do not deviate too much from an arrangement along a regular n-gon.
Similar content being viewed by others
Article PDF
References
Barachet, L L. 1957. Graphic solution of the travelling salesman problem. Oper Res, 5, 841–845.
Bennett, M D. 1982. Nucleotypic basis of the spatial ordering of chromosomes in eukaryotes and the implications of the order for genome evolution and phenotypic variation. Dover, G. A. and Flavell, R. B. (eds.) In Genome Evolution, Academic Press, London and New York, pp. 239–261.
Callow, R S. 1985. Comments on Bennett's model of somatic chromosome disposition. Heredity, 54, 171–177.
Christofides, N. 1975. Graph Theory—An Algorithmic Approach, Academic Press, London, New York and San Francisco.
Heslop-Harrison, J S, and Bennett, M D. 1983a. Prediction and analysis of spatial order in haploid chromosome complements. Proc R Soc Lond B, 218, 211–223.
Heslop-Harrison, J S, and Bennett, M D. 1983b. The spatial order of chromosomes in root-tip metaphases of Aegilops umbellulata. Proc R Soc Lond, B, 218, 225–239.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dorninger, D., Timischl, W. Geometrical constraints on Bennett's predictions of chromosome order. Heredity 59, 321–325 (1987). https://doi.org/10.1038/hdy.1987.138
Received:
Issue Date:
DOI: https://doi.org/10.1038/hdy.1987.138
This article is cited by
-
Parallel Connectivity in Edge-Colored Complete Graphs: Complexity Results
Graphs and Combinatorics (2024)
-
Two Sufficient Conditions for 2-Connected Graphs to Have Proper Connection Number 2
Bulletin of the Malaysian Mathematical Sciences Society (2020)
-
Optimal proper connection of graphs
Optimization Letters (2020)
-
Genome and chromosome disposition at somatic metaphase in a Hordeum × Psathyrostachys hybrid
Heredity (1991)