Marker-assisted backcrossing is a powerful method for developing new cultivars. To develop genomic-wide markers, genotyping-by-sequencing (GBS) can be an efficient method. However, unrefined low-quality markers and missing data between markers can contribute to hampering the marker selection process, particularly in multi-way crosses. In this study, we aimed to calculate the recovery rate of offspring individuals and minimize errors that occur among a large number of markers. Initially, missing data were imputed by comparing samples using the k-nearest neighbor (k-NN) algorithm. Thereafter, low-quality single-nucleotide polymorphisms (SNPs) were corrected by applying the graphical representation method based on the k-NN algorithm in order of the SNPs in a chromosome designed for a multi-parental population. Four-way cross and double-backcrossed tomato BC₁F₁ (230 lines) and BC₂F₁ (96 lines) populations were genotyped by GBS. The genotype of samples of the BC₁F₁ and BC₂F₁ populations was determined based on the parental haplotype. Thus, the method of visualizing the genotype of offspring individuals, generated via crosses of multiple parents, not only improves estimation of the recovery rate but also facilitates easier selection in breeding programs.

In this study, phenotypic distribution of 15 major fruit quality traits were analyzed using 252 progenies derived from a cross between ‘Tano Red’ (seed) and ‘Ruby Seedless’ (seedless), to obtain basic data for improving the breeding efficiency of grapevine cultivars. Berry skin color was dark red-violet in 46.4% of the progenies, which is the color of ‘Tano Red’ and ‘Ruby Seedless’, and berry shape was elliptic in 48.4%. Most of the progenies were very juicy with soft flesh, and closely related to the characteristics of ‘Tano Red’. Seeds were well developed in 67.1% of the progenies, rudimentary in 30.1%, and 2.8% were seedless, with seed weight being less than 0.15 g in 84.9% of the progenies. Among the 15 fruit quality traits assessed, bunch density, ease of berry detachment from pedicel, berry weight, berry seed number, berry longitudinal diameter, berry transverse diameter, berry soluble solids, and berry acidity showed normal distributions. Heritability of berry weight, berry longitudinal diameter, berry transverse diameter, berry soluble solids, and berry acidity was 0.89, 0.82, 0.78, 0.86, and 0.93, respectively. Berry weight was positively correlated with seed weight (r = 0.486^**), presence of seeds (r = 0.483^**), and seed number (r = 0.211^**). Seed weight significantly increased with presence of seeds (r = 0.607^**) and seed number (r = 0.725^**). In addition, presence of seeds was positively correlated with seed number (r = 0.319^**). These results could be useful for the identification of quantitative trait loci associated with fruit quality to assist in grapevine breeding.