Translating Integer Factoring into Graph Coloring

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 2,  2016, pp.611-624
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.2.611
Title & Authors
Translating Integer Factoring into Graph Coloring
Jensen, Tommy Rene;

Abstract
This paper gives for every positive integer n an explicit construction of a graph G with fewer than $\small{15{\log}^2n-{\frac{5}{2}}{\log}n+28}$ vertices, such that there exists a nontrivial factoring of n if and only if G is 3-colorable.
Keywords
graph coloring;integer factorization;
Language
English
Cited by
References
1.
M. Agrawal, N. Kayal and N. Saxena, PRIMES is in P, Ann. Mathematics, 160, (2004), 781-793.

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.