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A combinatorial $K$-theory perspective on the Edge Reconstruction Conjecture in graph theory

Published 22 Feb 2024 in math.KT, math.AT, and math.CO | (2402.14986v2)

Abstract: We provide a framework for abstract reconstruction problems using the $K$-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 $K$-theory of categories with covering families.

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