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Oct 6, 2022 at 11:54 history edited Tony Huynh CC BY-SA 4.0
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Sep 23, 2022 at 9:45 comment added Tony Huynh For your now (deleted) question, such a partition is sometimes called a layered partition, since the parts can actually be chosen to be 'vertical paths' from a fixed BFS spanning tree. Thus, each part intersects each 'layer' of the tree at most once.
Sep 23, 2022 at 9:43 comment added Tony Huynh That's a good question. The proof is constructive, but I think the bounds on N can be quite bad. See arxiv.org/abs/2202.08870 for an algorithm that computes the decomposition.
Sep 23, 2022 at 9:33 history edited Tony Huynh CC BY-SA 4.0
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Sep 22, 2022 at 21:15 comment added ABIM Also are there quantitative estimates on the number N?
Sep 22, 2022 at 16:47 comment added ABIM Wow amazing answer! Thanks so much; this seems to be exactly what I was looking for (+ more since it has nice background + history) thanks a million :)
Sep 22, 2022 at 16:47 vote accept ABIM
Sep 22, 2022 at 16:40 history answered Tony Huynh CC BY-SA 4.0