Geodesic
Balanced triangulations on few vertices and an implementation of cross-flips
Lorenzo Venturello1
1Universität Osnabrück
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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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. As a result we exhibit a vertex minimal balanced triangulation of the real projective plane, of the dunce hat and of the real projective space, as well as several balanced triangulations of surfaces and 3-manifolds on few vertices. In particular we construct small balanced triangulations of the 3-sphere that are non-shellable and shellable but not vertex decomposable.
DOI : 10.37236/8394
Classification : 05E45, 57Q15, 52B05
Mots-clés : PL manifolds, bistellar flips, balanced simplicial complexes, shellability, simplicial posets

Lorenzo Venturello  1

1 Universität Osnabrück 
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     author = {Lorenzo Venturello},
     title = {Balanced triangulations on few vertices and an implementation of cross-flips},
     journal = {The electronic journal of combinatorics},
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Lorenzo Venturello. Balanced triangulations on few vertices and an implementation of cross-flips. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8394

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