In cultivated tetraploid potato, reduction to diploidy (dihaploidy) allows hybridization to diploid germplasm, introgression breeding, and may facilitate the production of inbreds. Pollination with haploid inducers yields maternal dihaploids, as well as triploid and tetraploid hybrids. It is not known if dihaploids result from parthenogenesis, entailing development of embryos from unfertilized eggs, or genome elimination, entailing missegregation and loss of paternal chromosomes. A sign of genome elimination is the occasional persistence of haploid inducer DNA in some of the dihaploids. We characterized the genomes of 1,001 putative dihaploids and 134 hybrids produced by pollinating tetraploid clones with three haploid inducers, IVP35, IVP101, and PL4. We detected inheritance of full or partial chromosomes from the haploid inducer parent in 0.87% of the overall dihaploid progeny, irrespective of the combination of parental genotypes. Chromosomal breaks commonly affected the paternal genome in the dihaploid and tetraploid progeny, but not in the triploid progeny. Residual haploid inducer DNA is consistent with genome elimination as the mechanism of haploid induction. Further, the fact that paternal chromosome breaks are specific to dihaploids and tetraploid progeny suggests that they may be specific to 2x sperms, and buttresses the hypothesis that 2x sperms facilitate genome elimination.