Séminaire Lotharingien de Combinatoire, 82B.104 (2019), 12 pp.
Lorenzo Venturello
Balanced triangulations on few vertices and an implementation of cross-flips
Abstract.
A d-dimensional simplicial complex is balanced if the underlying graph is (d+1)-colorable. We present an implementation of cross-flips, a set of local moves introduced by Izmestiev, Klee and Novik which connect any two PL-homeomorphic balanced combinatorial manifolds without boundary. As a result we exhibit a vertex-minimal balanced triangulation of the dunce hat and balanced triangulations of several surfaces and 3-manifolds on few vertices. In particular we obtain small balanced triangulations of the 3-sphere that are non-shellable or shellable but not vertex decomposable.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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