Complexity Results in Graph Reconstruction

Abstract

We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c ≥ 1 of deletion:

Reconstruction Algorithms for Permutation Graphs and Distance-Hereditary Graphs

“…In the same paper they proved many GI related complexity results. Hemaspaandra et al extended the results [10]. The authors presented a polynomial time PREIMAGE CONSTRUCTION algorithm for interval graphs [12].…”