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A quasi-polynomial bound for the diameter of graphs of polyhedra
Authors:
Gil Kalai and Daniel J. Kleitman
Journal:
Bull. Amer. Math. Soc. 26 (1992), 315-316
MSC (2000):
Primary 52B55
MathSciNet review:
1130448
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Abstract: The diameter of the graph of a d-dimensional polyhedron with n facets is at most
- [1]
David
Barnette, 𝑊ᵥ paths on 3-polytopes, J.
Combinatorial Theory 7 (1969), 62–70. MR 0248636
(40 #1887)
- [2]
George
B. Dantzig, Linear programming and extensions, Princeton
University Press, Princeton, N.J., 1963. MR 0201189
(34 #1073)
- [3]
Branko
Grünbaum, Convex polytopes, With the cooperation of
Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics,
Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York,
1967. MR
0226496 (37 #2085)
- [4]
Gil
Kalai, Upper bounds for the diameter and height of graphs of convex
polyhedra, Discrete Comput. Geom. 8 (1992),
no. 4, 363–372. MR 1176376
(93i:52017), http://dx.doi.org/10.1007/BF02293053
- [5]
Victor
Klee and Peter
Kleinschmidt, The 𝑑-step conjecture and its relatives,
Math. Oper. Res. 12 (1987), no. 4, 718–755. MR 913867
(89a:52018), http://dx.doi.org/10.1287/moor.12.4.718
- [6]
Victor
Klee and David
W. Walkup, The 𝑑-step conjecture for polyhedra of dimension
𝑑<6, Acta Math. 117 (1967), 53–78.
MR
0206823 (34 #6639)
- [7]
D.
G. Larman, Paths of polytopes, Proc. London Math. Soc. (3)
20 (1970), 161–178. MR 0254735
(40 #7942)
- [1]
- D. W. Barnette,
paths on 3-polytopes, J. Combin. Theory 7 (1969), 62-70. MR 0248636 (40:1887)
- [2]
- G. B. Dantzig, Linear programming and extensions, Princeton Univ. Press, Princeton, NJ 1963. MR 0201189 (34:1073)
- [3]
- B. Grübaum, Convex polytopes, Wiley Interscience, London, 1967. MR 0226496 (37:2085)
- [4]
- G. Kalai, Upper bounds for the diameter and height of polytopes, Discrete Comput. Geom. 7(1992) (to appear). MR 1176376 (93i:52017)
- [5]
- V. Klee and P. Kleinschmidt, The d-steps conjecture and its relatives, Math. Operation Research 12 (1987), 718-755. MR 913867 (89a:52018)
- [6]
- V. Klee and D. Walkup, The d-step conjecture for polyhedra of dimension
, Acta Math. 133(1967), 53-78. MR 0206823 (34:6639)
- [7]
- D. G. Larman, Paths on polytopes, Proc. London Math. Soc. (3) 20 (1970), 161-178. MR 0254735 (40:7942)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1992-00285-9
PII:
S 0273-0979(1992)00285-9
Article copyright:
© Copyright 1992 American Mathematical Society
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