What's the name of rooted trees in which arbitrary connections between vertices of consecutive levels are allowed? (The level of a vertex is its distance to the root.) I.e.: All parents of a vertex have the same level. (Trees are characterized by its non-root vertices having exactly one parent.)
2026-03-27 15:07:48.1774624068
Graphs that are almost trees
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It looks like what you are after are (tooted) bipartite graphs. The graphs you describe are clearly pibartie (via the parity of noe distance to root) and each bipartite graph can be turned into such a "multi-parent tree" by assigning each node into the level given by its distance from a selected root node.