How to describe/name all the paths in an undirected graph where every node has no more than two neighbors?

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I am modeling a road network as a graph, using GPS data, etc.

A typical fraction of my graph would look like below:

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What I would like is to partition this graph as a list of node sequences, where every red dot would be used to split the network, generating a collection of simple polylines, so that every polyline would have a red dot in each endpoint, and no red dot inside the polyline.

I tried to ask some questions (1, 2) regarding this problem in StackOverflow, but I'm afraid I'm not using the appropriate terminology.