# 3-Regular Graphs Are 2-Reconstructible

## TL;DR

This paper proves that 3-regular graphs can be uniquely reconstructed from their subgraphs obtained by deleting two vertices, advancing understanding of graph reconstructibility.

## Contribution

It establishes that all 3-regular graphs are 2-reconstructible, filling a gap in the theory of graph reconstruction.

## Key findings

- 3-regular graphs are 2-reconstructible
- The result applies to all 3-regular graphs
- Advances the graph reconstruction conjecture

## Abstract

A graph is $\ell$-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting $\ell$ vertices. We prove that $3$-regular graphs are $2$-reconstructible.