Reductions among polynomial isomorphism types

Reductions of Graph Isomorphism Problems

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 c...

Graph isomorphism is polynomial

We show that the graph isomorphism problem is determined in a polynomial time. This is done by showing that that two graphs on n vertices are isomorphic if and only if a corresponding system of (4n− 1)n equations in n nonnegative variables is solvable. 2000 Mathematics Subject Classification: 03D15, 05C50, 05C60, 15A48, 15A51, 15A69, 90C05.

Isomorphism Types of Trees1

Strong Reductions and Isomorphism of Complete Sets

We study the structure of the polynomial-time complete sets for NP and PSPACE under strong nondeterministic polynomial-time reductions (SNP-reductions). We show the following results. • If NP contains a p-random language, then all polynomial-time complete sets for PSPACE are SNP-isomorphic. • If NP ∩ co-NP contains a p-random language, then all polynomial-time complete sets for NP are SNP-isomo...

Subgraph Isomorphism in Polynomial Time

In this paper, we propose a new approach to the problem of subgraph isomorphism detection. The new method is designed for systems which di erentiate between graphs that are a priori known, so-called model graphs, and unknown graphs, so-called input graphs. The problem to be solved is to nd a subgraph isomorphism from an input graph, which is given on-line, to any of the model graphs. The new me...