English

Optimally reconstructing caterpillars

Combinatorics 2021-12-07 v2

Abstract

For a graph GG, the \ell-deck of GG is the multiset of induced subgraphs on GG having \ell vertices. Recently, Groenland et al. proved that any tree can be reconstructed from its (8/9+o(1))n(8/9+o(1))n-deck. For the particular case of caterpillar graphs, we show that the (1/2+o(1))n(1/2+o(1))n-deck suffices, which is asymptotically tight.

Keywords

Cite

@article{arxiv.2112.01094,
  title  = {Optimally reconstructing caterpillars},
  author = {Zach Hunter},
  journal= {arXiv preprint arXiv:2112.01094},
  year   = {2021}
}

Comments

20 pages, comments welcome! (fixed typos on pages 1, 7, 9, 10 and the bibliography)

R2 v1 2026-06-24T08:01:10.813Z