paper

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

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