The graph isomorphism disease

Abstract

AbstractThe graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP‐completeness. No efficient (i.e., polynomial‐bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four‐color conjecture which prompted Harary to rechristen it the “four‐color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP‐completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.