Nonemptiness problems of Wang tiles with three colors

When p≥5, Wang's conjecture is known to be wrong. When p=2, the conjecture is true. This study proves that when p=3, the conjecture is also true. If P(B)≠∅, then B has a subset B′ of minimal cycle generators such that P(B′)≠∅ and P(B″)=∅ for B″⫋B′. This study demonstrates that the set C(3) of all minimal cycle generators contains 787,605 members that can be classified into 2,906 equivalence classes. N(3) is the set of all maximal non-cycle generators: if B∈N(3), then P(B)=∅ and P(B˜)≠∅ for B˜⫌B. Wang's conjecture is shown to be true by proving that B∈N(3) implies Σ(B)=∅.