Taiwanese Journal of Mathematics

SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS

V. Ejov, J. A. Filar, S. K. Lucas, and J. L. Nelson

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Abstract

In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.

Article information

Source
Taiwanese J. Math., Volume 10, Number 2 (2006), 327-338.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403828

Digital Object Identifier
doi:10.11650/twjm/1500403828

Mathematical Reviews number (MathSciNet)
MR2208270

Zentralblatt MATH identifier
1101.05042

Subjects
Primary: 05C45: Eulerian and Hamiltonian graphs 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 68W30: Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 68R10: Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35]

Keywords
Hamiltonian cycle Gröbner bases symbolic algebra

Citation

Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L. SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS. Taiwanese J. Math. 10 (2006), no. 2, 327--338. doi:10.11650/twjm/1500403828. https://projecteuclid.org/euclid.twjm/1500403828


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