Reductions of graph isomorphism problems

Abstract

We present a reduction between subgraph isomorphism and minimal partial subgraph isomorphism. We also provide a new reduction between graph isomorphism and minimal partial graph isomorphism. The new reduction is more efficient and simpler than the previous reduction and can be generalized to subgraph isomorphism. In addition, we show that a reduction from graph isomorphism that makes only one call to an oracle that finds a minimal partial isomorphism exists only if graph isomorphism is in P. We also provide a generalization of the result.