On some properties of three-index transportation polytopes
Diskretnaya Matematika, Tome 11 (1999) no. 3, pp. 109-125
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For any three-index planar transportation polytope (3-PTP) $M$
of order $m\times n\times k$ and dimensionality $d$,
we give a three-index axial transportation polytope (3-ATP)
$M'$ of order $mk\times nk\times mn$, with a
$d$-face which is combinatorially equivalent to the polytope $M$,
and vice versa, for any 3-ATP $M$ of order
$m\times n\times k$ we give a 3-PTP $M'$ of order
$(m+1)\times (n+1)\times (k+1)$, with
an $(mnk-m-n-k+2)$-face which is combinatorially equivalent to the polytope
$M$. With the use of these results, we present a series of new properties
of three-index transportation polytopes.
The research was supported by the Foundation for Basic Research of Republic Byelarus,
grant $\Phi$95-70.
@article{DM_1999_11_3_a9,
author = {M. A. Kravtsov and A. P. Krachkovskii},
title = {On some properties of three-index transportation polytopes},
journal = {Diskretnaya Matematika},
pages = {109--125},
publisher = {mathdoc},
volume = {11},
number = {3},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1999_11_3_a9/}
}
M. A. Kravtsov; A. P. Krachkovskii. On some properties of three-index transportation polytopes. Diskretnaya Matematika, Tome 11 (1999) no. 3, pp. 109-125. http://geodesic.mathdoc.fr/item/DM_1999_11_3_a9/