A133575 Table, read by rows, giving the number of vertices possible in 2 X n nondegenerate classical transportation polytopes.

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, 27, 28, 29, 30

Offset: 3

Author

Jonathan Vos Post, Sep 17 2007

Keywords

• nonn
• tabf
• more

Comments

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.

Examples

			Table 1 of De Loera et al.
size |dimension|Possible numbers of vertices
2.X.3|....2....|3.4..5..6
2.X.4|....3....|4.6..8.10.12
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
		

Links

• J. A. De Loera, Edward D. Kim, Shmuel Onn and Francisco Santos, Graphs of Transportation Polytopes, arXiv:0709.2189 [math.CO], 2007-2009, tables p. 4.

Crossrefs

Cf. A133575, A133576, A133577.