# Translating Integer Factoring into Graph Coloring

Jensen, Tommy Rene

• Accepted : 2015.11.02
• Published : 2016.06.23
• 18 11

#### Abstract

This paper gives for every positive integer n an explicit construction of a graph G with fewer than $15{\log}^2n-{\frac{5}{2}}{\log}n+28$ vertices, such that there exists a nontrivial factoring of n if and only if G is 3-colorable.

#### Keywords

graph coloring;integer factorization

#### References

1. M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Ann. Mathematics, 160, (2004), 781-793. https://doi.org/10.4007/annals.2004.160.781
2. T. R. Jensen and B. Toft, Graph Coloring Problems, Wiley Interscience, 1995.
3. M. R. Garey and D. S. Johnson, Computers and Intractability, W. H. Freeman, 1979.
4. A. K. Lenstra, Integer Factoring, Designs, Codes and Cryptography, 19 (2000), 101-128. https://doi.org/10.1023/A:1008397921377

#### Acknowledgement

Supported by : Kyungpook National University