The number of edges that need to be removed from a graph to disconnect it is called the edge-connectivity. Similarly, given a graph of genus $n>0$, there is a minimum number of edges that you have to remove to obtain a graph of genus $n-1$. Is there a name for this number?
Is there a name for the number of edges that need to be removed to lower the genus of a graph?
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graph-theory
terminology
topological-graph-theory
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0@RickDecker I was thinking that an alternative definition would focus on embeddings. Thus, given an embedding of genus $n$ (not necessarily a minimum genus embedding), I could ask for the minimum number of edges that need to be removed from the embedding to obtain an embedding of genus $n-1$. I am asking a related question [here](http://math.stackexchange.com/q/156182/10063) – 2012-06-11