## Project Details

### Description

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.

Status | Finished |
---|---|

Effective start/end date | 2018/08/01 → 2019/07/31 |

### Keywords

- P_4 decomposition
- graph partition
- graph design
- prime sum graph
- prime difference graph
- hamiltonian cycle

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