The number of genes involved in gene interaction is minimum
Gene interaction by definition requires contribution of at least two distinct genetic loci influencing same phenotypic trait; single gene governs monogenic trait without interaction, displaying dominance, incomplete dominance, or codominance. With two genes, possibilities for epistatic masking, complementation, additive effects emerge, generating modified dihybrid ratios like 9:7, 12:3:1, 15:1, 13:3. Minimum two genes produce four gamete types and sixteen F2 combinations necessary to detect interaction patterns experimentally. Adding third or more loci increases complexity toward polygenic net
Ref: Hartl & Jones, Genetics, 8th ed., Chapter 5: Minimum Number of Loci for Gene Interaction