A combinatorial -theory perspective on the Edge Reconstruction Conjecture in graph theory
arXiv:2402.14986 · doi:10.4310/HHA.2025.v27.n1.a16
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.
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