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Results tagged with simplicial-complexes
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user 4558
20
votes
2
answers
881
views
Is there an analogue of the Erdős–Gallai theorem for simplicial complexes?
The Erdős–Gallai theorem gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.
In particular $d_1 \ge d_2 \ge \dots \ge d_n$ …
- 7,857
10
votes
2
answers
441
views
Higher-dimensional Fáry's theorem?
Fáry's theorem says that every finite simple planar graph admits a planar embedding with straight line edges.
For which $(k,d)$ is it true that every finite $k$-dimensional simplicial complex embeddab …
- 7,857
16
votes
2
answers
2k
views
How many triangulations of the genus $g$ surface on $n$ vertices?
By "a triangulation of $X$", I mean a simplicial complex whose geometric realization is homeomorphic to $X$. Tutte showed that the number of combinatorially distinct triangulations $t(n)$ of the $2$-d …
- 7,857