Kyungpook Mathematical Journal

  • 제56권2호
  • /
  • Pages.611-624
  • /
  • 2016
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Translating Integer Factoring into Graph Coloring

  • 투고 : 2015.03.04
  • 심사 : 2015.11.02
  • 발행 : 2016.06.23
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초록

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.

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참고문헌

  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