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Гиперметрический конус и многогранник на графах

https://doi.org/10.22405/2226-8383-2019-20-2-169-177

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Об авторе

Мэтью Дютур-Сикирич

Хорватия


Список литературы

1. F. Barahona. The max-cut problem on graphs not contractible to Ks Oper. Res. Lett., 2(3):107–111, 1983.

2. F. Barahona. On cuts and matchings in planar graphs. Math. Programming, 60(1, Ser. A):53–68, 1993.

3. E. P. Baranovskiĭ. Volumes of L-simplexes of five-dimensional lattices. Mat. Zametki, 13:771–782, 1973.

4. E. P. Baranovskii. About l-simplexes of 6-dimensional lattices (in russian). In Second International conference “Algebraic, Probabilistic, Geometrical, Combinatorial and Functional Methods in the theory of numbers. 1995.

5. E. P. Baranovskii. The conditions for a simplex of 6-dimensional lattice to be l-simplex (in russian). Nauch. Trud. Ivan., (2):18–24, 1999.

6. A. Deza, B. Goldengorin, and D. V. Pasechnik. The isometries of the cut, metric and hypermetric cones. J. Algebraic Combin., 23(2):197–203, 2006.

7. M. Deza and M. Dutour. The hypermetric cone on seven vertices. Experiment. Math., 12(4):433–440, 2003.

8. M. Deza and M. Dutour Sikirić. The hypermetric cone and polytope on eight vertices and some generalizations. J. Symbolic Comput., 88:67–84, 2018.

9. M. Deza, V. P. Grishukhin, and M. Laurent. Extreme hypermetrics and L-polytopes. In Sets, graphs and numbers (Budapest, 1991), volume 60 of Colloq. Math. Soc. J’anos Bolyai, pages 157–209. North-Holland, Amsterdam, 1992.

10. M. Deza, V. P. Grishukhin, and M. Laurent. Hypermetrics in geometry of numbers. In Combinatorial optimization (New Brunswick, NJ, 1992–1993), volume 20 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 1–109. Amer. Math. Soc., Providence, RI, 1995.

11. M. Deza and M. D. Sikirić. Enumeration of the facets of cut polytopes over some highly symmetric graphs. Int. Trans. Oper. Res., 23(5):853–860, 2016.

12. M. M. Deza and M. Laurent. Geometry of cuts and metrics, volume 15 of Algorithms and Combinatorics. Springer, Heidelberg, 2010. First softcover printing of the 1997 original [MR1460488].

13. M. Dutour. The six-dimensional Delaunay polytopes. European J. Combin., 25(4):535–548, 2004.

14. M. Dutour Sikirić. The seven dimensional perfect Delaunay polytopes and Delaunay simplices. Canad. J. Math., 69(5):1143–1168, 2017.

15. M. Dutour Sikirić, M.-M. Deza, and E. I. Deza. Computations of metric/cut polyhedra and their relatives. In Handbook of geometric constraint systems principles, Discrete Math. Appl. (Boca Raton), pages 213–231. CRC Press, Boca Raton, FL, 2019.

16. M. Dutour Sikirić and V. Grishukhin. How to compute the rank of a Delaunay polytope. European J. Combin., 28(3):762–773, 2007.

17. M. Dutour Sikirić, A. Schürmann, and F. Vallentin. Inhomogeneous extreme forms. Ann. Inst. Fourier (Grenoble), 62(6):2227–2255 (2013), 2012.

18. R. Erdahl. A cone of inhomogeneous second-order polynomials. Discrete Comput. Geom., 8(4):387–416, 1992.

19. U. Fincke and M. Pohst. Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math. Comp., 44(170):463–471, 1985.

20. S. S. Ryshkov and E. P. Baranovskii. Repartitioning complexes in n-dimensional lattices (with full description for n ≤ 6). In Proceedings of conference "Voronoi impact on modern science Book 2, pages 115–124. 1998.

21. P. D. Seymour. Matroids and multicommodity flows. European J. Combin., 2(3):257–290, 1981.


Для цитирования:


Дютур-Сикирич М. Гиперметрический конус и многогранник на графах. Чебышевский сборник. 2019;20(2):169-177. https://doi.org/10.22405/2226-8383-2019-20-2-169-177

For citation:


Dutour M. The hypermetric cone and polytope on graphs. Chebyshevskii Sbornik. 2019;20(2):169-177. https://doi.org/10.22405/2226-8383-2019-20-2-169-177

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