On maximal instances for the original syntenic distance

AbstractThe syntenic distance between two genomes has been introduced by Ferretti, Nadeau and Sankoff as an approximation of the evolutionary distance between genomes for which the gene order is not known. This distance is the minimum number of fusions, fissions and translocations required to transform a genome into another. Kleinberg and Liben-Nowell, as well as Pisanti and Sagot, proved independently that for genomes with n chromosomes the diameter for this distance is 2n−4. Pisanti and Sagot also generalized this result, showing that the maximal distance between a genome with m chromosomes and a genome with n chromosomes is n+m−4. Kleinberg and Liben-Nowell asked for a characterization of maximal instances for the syntenic distance (pairs of n-chromosome genomes at a distance of 2n−4). In this paper, we give such a characterization, and show that we can extend it to pairs of genomes with, respectively, n and m chromosomes that are at maximal distance