圖形中傳遞數與填色數之性質研究

In graph theory, we prove that any proper edge coloring of K_n has a P_4 decomposition. Even if the number of edges of K_n can't divide by 3 and the left edge can be in any place of the complete graph K_n. In number theory, we prove the prime sum graph of n vertices plus some additional condition has hamiltonian cycle. Besides, the prime difference graph of n vertices is hamiltonian and has hamiltonian path even if the ends of the vertices is arbitrarily assigned. These is the best result in the fields so far.