Optimally reconstructing caterpillars
Abstract
For a graph G, the -deck of G is the multiset of induced subgraphs on G having 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.
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