Autumn crocuses, Colchicum autumnale, are in bloom in several of the beds at Paulik Park. If you took biology in high school or university, Colchicum may ring a bell. This plant was the original source for colchicine, a compound used in cell biology to block spindle formation during cell division, which prevents the contracted chromosomes from segregating, a necessity for daughter cells to receive the correct number of chromosomes.
For this reason it has many medicinal applications, but watermelons are more interesting. If chromosome segregation is inhibited during meiosis, which usually results in four haploid gametes, two of the gametes will be diploid whereas the other two will contain no chromosomes. If two diploid gametes are combined, a tetraploid (twice the normal number of chromosomes) zygote will result. In animals this is usually fatal, but it can be a boon to plant growth and development. Then, if a tetraploid plant is crossed with a diploid plant, triploid offspring (thrice the normal number of chromosomes) will result, which are sterile, but if pollinated with pollen from a diploid plant can create seedless fruits.
Voila. Seedless watermelons.