Geodesic
Flip graphs of stacked and flag triangulations of the 2-sphere
Benjamin Burton1 ; Basudeb Datta2 ; Jonathan Spreer3
1The University of Queensland, Brisbane
2Indian Institute of Science, Bangalore
3The University of Sydney
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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It is well-known that the flip graph of $n$-vertex triangulated $2$-spheres is connected, i.e., each pair of $n$-vertex triangulated $2$-spheres can be turned into each other by a sequence of edge flips for each $n\ge 4$. In this article, we study various induced subgraphs of this graph. In particular, we prove that the subgraph of $n$-vertex flag $2$-spheres distinct from the double cone is still connected. In contrast, we show that the subgraph of $n$-vertex stacked $2$-spheres has at least as many connected components as there are trees on $\lfloor\frac{n-5}{3}\rfloor$ nodes with maximum node-degree at most four.
DOI : 10.37236/10292
Classification : 57Q15, 05C10
Mots-clés : triangulated 2-sphere, planar triangulation, flip graph, Pachner graph, edge flip, flag 2-sphere, stacked 2-sphere.

Benjamin Burton  1   ; Basudeb Datta  2   ; Jonathan Spreer  3

1 The University of Queensland, Brisbane
2 Indian Institute of Science, Bangalore
3 The University of Sydney 
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Benjamin Burton; Basudeb Datta; Jonathan Spreer. Flip graphs of stacked and flag triangulations of the 2-sphere. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10292

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