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Open access

Gábor Mészáros

Abstract

We study the inheritance of path-pairability in the Cartesian product of graphs and prove additive and multiplicative inheritance patterns of path-pairability, depending on the number of vertices in the Cartesian product. We present path-pairable graph families that improve the known upper bound on the minimal maximum degree of a path-pairable graph. Further results and open questions about path-pairability are also presented.

Open access

Gábor Mészáros

Summary

The characterization of livestock genetic diversity has experienced extensive changes with the availability of dense nucleotide markers. Among the various forms of markers, the single nucleotide polymorphisms (SNP) have arguably the largest influence. A wide range of indicators for the assessment of genetic diversity was developed, or the existing methods were improved, enabling us to make informed decisions on the management of livestock populations. This review discusses the selected aspects of diversity assessment, with special attention to the SNP based methods.

One of the core concepts in genomics of diversity is the linkage disequilibrium (LD), as it was shaped by demographic events during the development of breeds and species. These events, either natural or artificial, left detectable signals within the livestock genomes. Further changes were induced by human activity when mating related animals, leading to fixing or improving the desired traits in the breed, but reducing their genetic variability. The assessment of relatedness is also pivotal to construct meaningful mating plans and to avoid the negative consequences of inbreeding depression that might be detrimental especially in small, endangered populations. Both LD and relatedness are of interest on their own, as well as in their follow-up applications deriving overall measures of effective population size.