## Pacific Journal of Mathematics

### On the graph structure of convex polyhedra in $n$-space.

M. L. Balinski

#### Article information

Source
Pacific J. Math. Volume 11, Number 2 (1961), 431-434.

Dates
First available in Project Euclid: 14 December 2004

http://projecteuclid.org/euclid.pjm/1103037323

Mathematical Reviews number (MathSciNet)
MR0126765

Zentralblatt MATH identifier
0103.39602

Subjects
Primary: 52.10
Secondary: 90.10

#### Citation

Balinski, M. L. On the graph structure of convex polyhedra in $n$-space. Pacific J. Math. 11 (1961), no. 2, 431--434. http://projecteuclid.org/euclid.pjm/1103037323.

#### References

• [1] Michel L. Balinski, An Algorithm for Finding all Vertices of Convex Polyhedral Sets, doctoral dissertation, Princeton Universty, June, 1959. J. Soc. Indust. Applied Math., 9 (1961), 72-88.
• [2] T. A. Brown, HamiltonianPaths on Convex Polyhera, unpublished note, The RAND Corporation, August 1960, (included while in press).
• [3] G. B. Dantzig and D. R. Fulkerson, On the Max-Flow Min-Cut Theorem ofNetworks, paper 12 of Liner Inequalities and Related Systems, H. W. Kuhn and A. W. Tucker (eds.) Annals of Mathematics No. 38, Princeton University Press, Princeton, N.J., 1956.
• [4] G. A. Dirac, Some theorems of abstract graphs, Proc. London Math. Soc, Series 3, Vol. II (1952), 69-81.
• [5] L. R. Ford, Jr. and D. R. Fulkerson, Maximal flow through a network, Canadian Math., 8 (1956), 399-404.
• [6] A. W. Tucker, Linear Inequalities and Convex Polyhedral Sets, Proceedings of the Second Symposium in Linear Programming, Bureau of Standards, Washington, D. C, January 27-29, 1955, pp. 569-602.
• [7] W. T. Tutte, On Hamiltonian circuits, Journal London Math. Soc, 21 (1946), 98-101.
• [8] Hassler Whitney, Congruent graphs and the connectivity of graphs, Amer. J. Math., 54 (1932), 150-168.