A combinatorial $K$-theory perspective on the Edge Reconstruction Conjecture in graph theory
K-Theory and Homology
2025-06-17 v2 Algebraic Topology
Combinatorics
Abstract
We provide a framework for abstract reconstruction problems using the -theory of categories with covering families, which we then apply to reformulate the edge reconstruction conjecture in graph theory. Along the way, we state some fundamental theorems for the -theory of categories with covering families.
Cite
@article{arxiv.2402.14986,
title = {A combinatorial $K$-theory perspective on the Edge Reconstruction Conjecture in graph theory},
author = {Maxine E. Calle and Julian J. Gould},
journal= {arXiv preprint arXiv:2402.14986},
year = {2025}
}
Comments
24 pages. Added Section 4 with suggestions for future research directions and made minor changes to the exposition. Final version to appear in Homology, Homotopy and Applications