The Edge Reconstruction Conjecture and Combinatorial K-theory -
Given a finite graph, imagine all the ways you can obtain a subgraph by deleting a single edge. Can you uniquely reconstruct your original graph from just this collection of subgraphs? This question is known as the Edge Reconstruction Conjecture and is a famous open problem in graph theory. In this talk, we will discuss how to rephrase this reconstruction problem more algebraically, using the framework of combinatorial K-theory. This talk is based on joint work with J. J. Gould.