## Polytope Skeletons And Paths

Venue: | HANDBOOK OF DISCRETE AND COMPUTATIONAL GEOMETRY (SECOND EDITION ), CHAPTER 20 |

Citations: | 6 - 0 self |

### BibTeX

@INPROCEEDINGS{Kalai_polytopeskeletons,

author = {Gil Kalai},

title = {Polytope Skeletons And Paths},

booktitle = {HANDBOOK OF DISCRETE AND COMPUTATIONAL GEOMETRY (SECOND EDITION ), CHAPTER 20},

year = {},

pages = {455--476},

publisher = {CRC Press LLC, Boca}

}

### OpenURL

### Abstract

### Citations

389 | A Separator Theorem for Planar Graphs - Lipton, Tarjan - 1979 |

275 | Every planar map is four-colorable - Appel, Haken - 1976 |

224 | Regular polytopes - Coxeter - 1973 |

180 |
Lectures on Polytopes, Graduate texts in mathematics 152
- Ziegler
- 1994
(Show Context)
Citation Context ...olytopal graphs with many references (most references for the results in Section 17.1 and related results can be found there). More material on the topic of this chapter can also be found in [Gru67], =-=[Zie95]-=-, [KK96], and [BL93]. The references in Ziegler's book [Zie95] and their electronic updates cover most of the results described in this chapter. For a survey on the Hirsch conjecture and its relatives... |

169 | How good is the simplex algorithm - Klee, Minty - 1972 |

144 | Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time - Spielman, Teng - 2001 |

122 | Lectures on Polytopes, volume 152 of Graduate Texts in Mathematics - Ziegler - 1995 |

113 | The four-colour theorem - Robertson, Sanders, et al. - 1997 |

111 | A census of planar triangulations - Tutte - 1962 |

100 | Homology and shellability of matroids and geometric lattices - Björner - 1992 |

91 | A Theorem on Planar Graphs - Tutte - 1956 |

82 | Finding Small Simple Cycle Separators for 2-Connected Planar Graphs - Miller - 1986 |

80 | Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie. Reprint der 1934 Auflage. Grundlehren der Mathematischen Wissenschaften - Steinitz, Rademacher - 1976 |

74 | Balanced matroids - Feder, Mihail - 1992 |

72 | Separators for sphere-packings and nearest neighbor graphs - Miller, Teng, et al. - 1997 |

68 | Shellable decompositions of cells and spheres - Bruggesser, Mani - 1971 |

68 | Non-separable and planar graphs - Whitney - 1932 |

54 | Quantum Geometry - AMBJØRN, DURHUUS, et al. - 1997 |

50 | A quasi-polynomial bound for the diameter of graphs of polyhedra - Kalai - 1992 |

49 | Rigidity and the lower bound theorem - Kalai - 1987 |

48 |
The d-step conjecture and its relatives
- Klee, Kleinschmidt
- 1987
(Show Context)
Citation Context ...6], and [BL93]. The references in Ziegler's book [Zie95] and their electronic updates cover most of the results described in this chapter. For a survey on the Hirsch conjecture and its relatives, see =-=[KK87]-=-. More recent results can be found in Kleinschmidt's chapter in [BMS + 94] and in [Zie95, Section 3.3]. Related results on simplex algorithms are mentioned in Chapter 38 of this Handbook. Martini's Ch... |

43 |
Convex polytopes, Interscience
- Grünbaum
- 1967
(Show Context)
Citation Context ...rvey on polytopal graphs with many references (most references for the results in Section 17.1 and related results can be found there). More material on the topic of this chapter can also be found in =-=[Gru67]-=-, [Zie95], [KK96], and [BL93]. The references in Ziegler's book [Zie95] and their electronic updates cover most of the results described in this chapter. For a survey on the Hirsch conjecture and its ... |

38 | A simple way to tell a simple polytope from its graph - Kalai - 1988 |

38 | Decompositions of simplicial complexes related to diameters of convex polyhedra - Billera, Provan - 1980 |

29 | The diameter of graphs of convex polytopes and f-vector theory, in “Applied Geometry and Discrete Mathematics, The Victor Klee Festschrift - Kalai - 1991 |

28 | On the graph structure of convex polyhedra in n-space - Balinski - 1961 |

28 | Trees in Polyhedral Graphs - Barnette - 1966 |

25 | Combinatorial aspects of convex polytopes
- Bayer, Lee
- 1993
(Show Context)
Citation Context ...many references (most references for the results in Section 17.1 and related results can be found there). More material on the topic of this chapter can also be found in [Gru67], [Zie95], [KK96], and =-=[BL93]-=-. The references in Ziegler's book [Zie95] and their electronic updates cover most of the results described in this chapter. For a survey on the Hirsch conjecture and its relatives, see [KK87]. More r... |

25 | Mani–Levitska: On puzzles and polytope isomorphisms - Blind, P - 1987 |

25 | Contribution to the theory of Eulerian polyhedra - Kotzig - 1955 |

25 | Nagel: Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers - Migliore, U |

24 | The Hirsch conjecture is true for (0,1)-polytopes - Naddef - 1989 |

23 | Infinitesimally rigid polyhedra I. Statics of frameworks, Trans - Whiteley - 1984 |

22 | Hyperplane arrangements with a lattice of regions - Björner, Edelman, et al. - 1990 |

21 | A proof of the strict monotone 4-step conjecture, in \Advances in discrete and computational geometry - Holt, Klee - 1999 |

21 | Unshellable triangulations of spheres - Lickorish - 1991 |

21 | Convex and linear orientations of polytopal graphs - Mihalisin, Klee - 1999 |

21 | Completely unimodal numberings of a simple polytope - Hoke - 1988 |

19 | The d-step conjecture for polyhedra of dimension d < 6 - Klee, Walkup - 1967 |

18 | Some aspects of the combinatorial theory of convex polytopes.” Polytopes: abstract, convex and computational - Kalai - 1993 |

17 | Equidecomposable and weakly neighborly polytopes - Bayer - 1993 |

17 | Zur Morphologie der Polyeder - Eberhard - 1891 |

16 | Neighborly cubical spheres and a cubical lower bound conjecture, IsraelJ.Math.,102(1997),pp.297–315 - Babson, Billera, et al. |

16 | Which spheres are shellable - Danaraj, Klee - 1978 |

16 | Many polytopes meeting the conjectured Hirsch bound - Holt, Klee - 1998 |

15 | Random walks, totally unimodular matrices, and a randomised dual simplex algorithm - Dyer, Frieze - 1994 |

15 | Decompositions of simplicial balls and spheres with knots consisting of few edges - HACHIMORI, ZIEGLER |

15 | Projectivites of simplicial complexes and colorings of simple polytopes - Joswig |

15 | Neighborly cubical polytopes, Discrete Comput. Geometry 24 (2000), 325–344, The Branko Grünbaum birthday issue - Joswig, Ziegler |

15 | Sur l’opération A de l’Analysis Situs - Kuratowski - 1922 |