# On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance

Feijão P, Martinez F, Thévenin A (2015) *BMC Bioinformatics* 16(Suppl 19): S1.

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Finding the smallest sequence of operations to transform one genome into another is an important problem in comparative genomics. The breakpoint graph is a discrete structure that has proven to be effective in solving distance problems, and the number of cycles in a cycle decomposition of this graph is one of the remarkable parameters to help in the solution of related problems. For a fixed k, the number of linear unichromosomal genomes (signed or unsigned) with n elements such that the induced breakpoint graphs have k disjoint cycles, known as the Hultman number, has been already determined. In this work we extend these results to multichromosomal genomes, providing formulas to compute the number of multichromosal genomes having a fixed number of cycles and/or paths. We obtain an explicit formula for circular multichromosomal genomes and recurrences for general multichromosomal genomes, and discuss how these series can be used to calculate the distribution and expected value of the rearrangement distance between random genomes.

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Article Processing Charge funded by the Deutsche Forschungsgemeinschaft and the Open Access Publication Fund of Bielefeld University.

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Feijão P, Martinez F, Thévenin A. On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance.

*BMC Bioinformatics*. 2015;16(Suppl 19): S1.Feijão, P., Martinez, F., & Thévenin, A. (2015). On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance.

*BMC Bioinformatics*,*16*(Suppl 19), S1. doi:10.1186/1471-2105-16-s19-s1Feijão, P., Martinez, F., and Thévenin, A. (2015). On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance.

*BMC Bioinformatics*16:S1.Feijão, P., Martinez, F., & Thévenin, A., 2015. On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance.

*BMC Bioinformatics*, 16(Suppl 19): S1. P. Feijão, F. Martinez, and A. Thévenin, “On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance”,

*BMC Bioinformatics*, vol. 16, 2015, : S1. Feijão, P., Martinez, F., Thévenin, A.: On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance. BMC Bioinformatics. 16, : S1 (2015).

Feijão, Pedro, Martinez, Fábio, and Thévenin, Annelyse. “On the distribution of cycles and paths in multichromosomal breakpoint graphs and the expected value of rearrangement distance”.

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### 1 Citation in Europe PMC

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