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%I #18 Jan 03 2016 10:41:46
%S 3,4,5,6,4,6,8,10,12,5,8,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30
%N Table, read by rows, giving the number of vertices possible in 2 X n nondegenerate classical transportation polytopes.
%C This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic bound on the diameter of axial 3-way transportation polytopes and a catalog of non-degenerate transportation polytopes of small sizes. The catalog disproves five conjectures about these polyhedra stated in the monograph by Yemelichev et al. (1984). It also allowed us to discover some new results. For example, we prove that the number of vertices of an m X n transportation polytope is a multiple of the greatest common divisor of m and n.
%H J. A. De Loera, Edward D. Kim, Shmuel Onn and Francisco Santos, <a href="http://arXiv.org/abs/0709.2189">Graphs of Transportation Polytopes</a>, arXiv:0709.2189 [math.CO], 2007-2009, tables p. 4.
%e Table 1 of De Loera et al.
%e size |dimension|Possible numbers of vertices
%e 2.X.3|....2....|3.4..5..6
%e 2.X.4|....3....|4.6..8.10.12
%e 2.X.5|....4....|5.8.11.12.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30
%Y Cf. A133575, A133576, A133577.
%K nonn,tabf,more
%O 3,1
%A _Jonathan Vos Post_, Sep 17 2007
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