论文信息 - Deciding constructibility of 3-balls with at most two interior vertices

Deciding constructibility of 3-balls with at most two interior vertices

Abstract In this paper, we treat the problem to find an efficient algorithm to decide constructibility. Such an algorithm was given only under the condition that the given simplicial complex is a triangulated 3-ball with all the vertices on the boundary [M. Hachimori, Non-constructible simplicial balls and a way of testing constructibility, Discrete Comput. Geom. 22 (1999) 223–230]. Here we extend this result to the case that the triangulated 3-ball has at most two interior vertices. Our algorithm runs in O(#facets) time. Also, we give an example which shows that the same strategy cannot be used for the cases with more than two interior vertices.

Masahiro Hachimori

[1] G. Ziegler,et al. Decompositions of simplicial balls and spheres with knots consisting of few edges , 2000 .

[2] J. W. Cannon,et al. Shrinking cell-like decompositions of manifolds. Codimension three , 1979 .

[3] Richard Ehrenborg,et al. Non-constructible Complexes and the Bridge Index , 2001, Eur. J. Comb..

[4] Michelle L. Wachs,et al. On lexicographically shellable posets , 1983 .

[5] Günter M. Ziegler,et al. Shelling Polyhedral 3-Balls and 4-Polytopes , 1998, Discret. Comput. Geom..

[6] P. McMullen. The maximum numbers of faces of a convex polytope , 1970 .

[7] Victor Klee,et al. A Representation of 2-dimensional Pseudomanifolds and its use in the Design of a Linear-Time Shelling Algorithm , 1978 .

[8] William Kazez,et al. Polyhedral minimal surfaces, Heegaard splittings, and decision problems for 3-dimensional manifolds , 1996 .

[9] A. Fomenko,et al. THE PROBLEM OF DISCRIMINATING ALGORITHMICALLY THE STANDARD THREE-DIMENSIONAL SPHERE , 1974 .

[10] Victor Klee,et al. Which Spheres are Shellable , 1978 .

[11] E. C. Zeeman,et al. Seminar on combinatorial topology , 1963 .

[12] P. Mani,et al. Shellable Decompositions of Cells and Spheres. , 1971 .

[13] G. Ziegler. Lectures on Polytopes , 1994 .

[14] Richard P. Stanley,et al. Cohen-Macaulay rings and constructible polytopes , 1975 .

[15] Masahiro Hachimori. Nonconstructible Simplicial Balls and a Way of Testing Constructibility , 1999, Discret. Comput. Geom..