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

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.