On the Maximum Number of Vertices of Minimal Embedded Graphs

Details On the Maximum Number of Vertices of Minimal Embedded Graphs On the Maximum Number of Vertices of Minimal Embedded Graphs

2009-10-13

arxiv.org/abs/0910.2469v1

Mathematics

Combinatorics

20 pages, 25 figures

Scientific paper

Consider graphs embedded in a Riemannian manifold, attached at $n$ fixed
points. Say such a graph is minimal if it is a critical point of the length
functional. In this paper, we give a sharp upper bound for the maximal number
of vertices of planar 3-regular minimal graphs.

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