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Essentially, it describes something like a neural network with adjacent layers being bipartite graphs. I am particularly interested in efficient algorithms to find some subset of vertices in layer 3 that are reachable through every edge from some input vertex in layer 1.

In my example graph, the first vertex in layer 3 satisfies this condition for every vertex in layer 1. The second vertex in layer 2 satisfies this condition for the second vertex in layer 1, but not the first and third vertices.

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    This is also just a bipartite graph – 2017-02-04
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    (all the even numbered layers together form one part, and the odd-numbered layers form a second part). Then only distinction is that you have partitioned the two parts of your bipartite graph into layers. – 2017-02-05
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    "...some subset of vertices in layer 3 that are reachable **through every edge** from some input vertex in layer 1." The bold part doesn't make sense to me since there are no edges from layer 1 to layer 3. Can you re-explain? – 2017-02-24
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    Well, there are tripartite (and, more generally, [multipartite](https://en.wikipedia.org/wiki/Multipartite_graph)) graphs. – 2017-02-24
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    @Casteels I should probably have phrased it better. There doesn't need to be an edge directly from layer 1 to layer 3, just along the path. – 2017-02-25

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