Shuffling the Deck: Invariant Theory and the Graph Reconstruction Conjecture
Combinatorics
2026-04-21 v1 Commutative Algebra
Abstract
The graph reconstruction conjecture asserts that every simple graph on at least three vertices is uniquely determined by its deck of vertex-deleted subgraphs. In this expository article we survey the conjecture and present an invariant-theoretic approach to studying it. The aim is to be able to show that polynomials that distinguish between decks also distinguish between original graphs, thus translating a graph-theoretic problem into an algebraic one.
Cite
@article{arxiv.2604.16567,
title = {Shuffling the Deck: Invariant Theory and the Graph Reconstruction Conjecture},
author = {Emilie Dufresne and Gabriela Jeronimo and Jenny Kenkel and Haydee Lindo and Nelly Villamizar},
journal= {arXiv preprint arXiv:2604.16567},
year = {2026}
}