Acyclic graphs with at least 2ℓ+1 vertices are ℓ-recognizable [article]

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West, Dara Zirlin
2021 arXiv   pre-print
The (n-ℓ)-deck of an n-vertex graph is the multiset of subgraphs obtained from it by deleting ℓ vertices. A family of n-vertex graphs is ℓ-recognizable if every graph having the same (n-ℓ)-deck as a graph in the family is also in the family. We prove that the family of n-vertex graphs having no cycles is ℓ-recognizable when n≥2ℓ+1 (except for (n,ℓ)=(5,2)). It is known that this fails when n=2ℓ.
arXiv:2103.12153v1 fatcat:3t7jdm5d7nf6thl3c3d5dukefm