Paper
Bell coloring graphs: realizability and reconstruction
Authors
Shamil Asgarli, Sara Krehbiel, Simon MacLean
Abstract
Given a graph , the Bell -coloring graph has vertices given by partitions of into independent sets (allowing empty parts), with two partitions adjacent if they differ only in the placement of a single vertex. We first give a structural classification of cliques in Bell coloring graphs. We then show that all trees and all cycles arise as Bell coloring graphs, while is not a Bell coloring graph and, more generally, is not an induced subgraph of any Bell coloring graph whenever . We also prove two reconstruction results: the Bell -coloring graph is a complete invariant for trees, and the Bell -coloring multigraph determines any graph up to universal vertices.