摘要: This paper introduces the notion of (r, s) incidence graph an n-polytope P as bipartite whose nodes correspond to r-faces and s-faces with edge joining two iff one corresponding faces contains other. Various types connectivity are defined for graphs bounds these connectivities established functions r, s, n. It is shown that also valid a large class cell-complexes.
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sci-hub.se 参考文章(7)
Karl Menger, Zur allgemeinen Kurventheorie Fundamenta Mathematicae. ,vol. 10, pp. 96- 115 ,(1927) , 10.4064/FM-10-1-96-115
Victor Klee, ON THE NUMBER OF VERTICES OF A CONVEX POLYTOPE Canadian Journal of Mathematics. ,vol. 16, pp. 701- 720 ,(1964) , 10.4153/CJM-1964-067-6
H. Weyl, Elementare Theorie der konvexen Polyeder Commentarii Mathematici Helvetici. ,vol. 7, pp. 290- 306 ,(1934) , 10.1007/BF01292722
H. G. Eggleston, Branko Grünbaum, Victor Klee, Some semicontinuity theorems for convex polytopes and cell-complexes Commentarii Mathematici Helvetici. ,vol. 39, pp. 165- 188 ,(1964) , 10.1007/BF02566949
Branko Grünbaum, On the facial structure of convex polytopes Bulletin of the American Mathematical Society. ,vol. 71, pp. 559- 561 ,(1965) , 10.1090/S0002-9904-1965-11329-5
G. A. Dirac, Extensions of Menger's Theorem† Journal of the London Mathematical Society. ,vol. s1-38, pp. 148- 161 ,(1963) , 10.1112/JLMS/S1-38.1.148
Michel Balinski, On the graph structure of convex polyhedra in n-space Pacific Journal of Mathematics. ,vol. 11, pp. 431- 434 ,(1961) , 10.2140/PJM.1961.11.431