## Abstract

The (Formula presented.) -deck of an (Formula presented.) -vertex graph is the multiset of subgraphs obtained from it by deleting (Formula presented.) vertices. A family of (Formula presented.) -vertex graphs is (Formula presented.) -recognizable if every graph having the same (Formula presented.) -deck as a graph in the family is also in the family. We prove that the family of (Formula presented.) -vertex graphs with no cycles is (Formula presented.) -recognizable when (Formula presented.) (except for (Formula presented.)). As a consequence, the family of (Formula presented.) -vertex trees is (Formula presented.) -recognizable when (Formula presented.) and (Formula presented.). It is known that this fails when (Formula presented.).

Original language | English (US) |
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Journal | Journal of Graph Theory |

DOIs | |

State | Accepted/In press - 2023 |

## Keywords

- acyclic graph
- deck
- graph reconstruction
- tree

## ASJC Scopus subject areas

- Geometry and Topology
- Discrete Mathematics and Combinatorics