Are there any Euclidean spaces, in which the maximal vertex degree of MSTs (Minimum Spanning Trees) of a finite set of points and edge weights equal to Euclidean distance, isn't equal to the [kissing number](https://en.wikipedia.org/wiki/Kissing_number_problem)? 


**Remark:**  

The fact, that the kissing number is an upper bound on the vertex degree of MSTs of Euclidean spaces can be exploited for reducing the memory footprint for calculating those MSTs; instead of feeding $\frac{n(n-1)}{2}$ distances into the MST algorithm, it suffices to provide only the $k$ smallest distances for each vertex, where $k$ is the kissing number of the respective Euclidean space.



Maximal Vertex Degree of MSTs in Euclidean Spaces
The answer (maybe)1 is no. In the following paper,


*Gabriel Robins and Jeffrey S. Salowe*, [**On the maximum degree of minimum spanning trees.**](http://dx.doi.org/10.1145/177424.177978) Proceedings of the tenth annual symposium on Computational Geometry (SCG '94), 250-258 (1994). [PDF](https://www.cs.virginia.edu/~robins/papers/cg94_camera3_final.pdf).



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> The authors proved that under the $L\_p$ norm, the maximum vertex degree over all MSTs is equal to the kissing number of the corresponding unit ball; 
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1 I said 'maybe', since I have not checked the proof of the mentioned paper.


