Optimally reconstructing caterpillars

Abstract

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

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

References in corpus (1)

• Acyclic graphs with at least $2\ell +1$ vertices are $\ell$-recognizable