
> 
> **Possible Duplicate:**  
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> [What is the max number of points in R^3, interconnected by generic curves?](https://mathoverflow.net/questions/9293/what-is-the-max-number-of-points-in-r3-interconnected-by-generic-curves) 
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Given a set of points connected by edges lying on an euclidean plane,
I'd like to find which is the smaller dimension of the euclidean space where the graph can lie without an overlapping of the edges. Is it a standard problem? Which mathematical tools I have to know to manage with this kind of problems?
I can obviously guess that I could always take $d=v-1$ where $v$ is the number of verticies
but I can't understand which is the smaller dimension.


Thanks



How many dimensions I need to embed a graph?
As Charles points out, you can always embed a graph in three dimensions. The interesting question is how complicated a **surface** one needs to embed a graph into. The number of handles one has to attach to a spehere in order for a graph to become embeddable is called the **genus** of the graph, see [graph embedding](http://en.wikipedia.org/wiki/Graph_embedding) on Wikipedia, which offers other useful information.


