This may be a stupid question, but is there a name for a directed acyclic graph in which:
- every node can be organized into separate, sequential "bins"
- any two adjacent "bins" of nodes are a (not necessarily connected) bipartite graph with all vertices directed to the "latter" bin
For example, take a wierd family tree where people give birth (to any number) and then immediately die every 10 years, and single people and threesomes (and n-somes) can produce any number of offspring too, and some are immaculate births. So the "bins" in this example would be the decades.
I guess also a run of Conway's Game of Life could be mapped with this kind of graph, with each iteration being a "bin".
I'd like to find a name so I can study the various ways of how it is applied in the real world and what special properties it would have as opposed to a more general DAG, so any info on those things is also appreciated. I hope I've properly described it...
Note that this is not the same as any DAG, for example, here's a DAG that's not this: a graph where "a" points to "b", "a" points to "c", and "b" points to "c"
I think your concept is the same as the cover digraph of a graded poset.