In this paper an improved version of a graph matching algorithm is presented, which is able to efficiently solve the graph isomorphism and graph-subgraph isomorphism problems on Attributed Relational Graphs. This version is particularly suited to work with very large graphs, since its memory requirements are quite smaller than those of other algorithms of the same kind. After a detailed descrip...

We reduce the graph isomorphism problem to 2-nilpotent p-groups isomorphism problem (and to finite 2-nilpotent Lie algebras the ring Z/pZ. Furthermore, we show that classifying problems in categories graphs, finite 2-nilpotent p-groups, and 2-nilpotent Lie algebras over Z/pZ are polynomially equivalent and wild.

Two graphs with adjacency matrices A and B are isomorphic if there exists a permutation matrix P for which the identity PAP = B holds. Multiplying through by P and relaxing the permutation matrix to a doubly stochastic matrix leads to the notion of fractional isomorphism. We show that the levels of the Sherali-Adams hierarchy of linear programming relaxations applied to fractional isomorphism i...

We define a category Fat whose objects are isomorphism classes of bordered fat graphs and show that its geometric realization is a classifying space for the bordered mapping class groups. We then construct a CW structure on this geometric realization with one cell per isomorphism classes of bordered fat graphs. Its cellular cochain complex gives a bordered graph complex which computes the integ...

The graph isomorphism problem consists in deciding if two given graphs have an identical structure. This problem may be modeled as a constraint satisfaction problem in a very straightforward way, so that one can use constraint programming to solve it. However, constraint programming is a generic tool that may be less e cient than dedicated algorithms which take advantage of the global semantic ...

A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. This paper develops systematically the theory of graph fibrations, emphasizing in particular those results that recently found application in the theory of distributed systems.

The concept of a k-pairable graph was introduced by Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In this talk, we introduce a special class of k-pairable graphs which are called uniquely pairable graphs. Then we give a characterization of uniquely pairable graphs in terms of the prime factor decomposi...

The P,-reducible graphs are a natural generalization of the well-known class of cographs, with applications to scheduling, computational semantics, and clustering. More precisely, the Pa-reducible graphs are exactly the graphs none of whose vertices belong to more than one chordless path with three edges. A remarkable property of P,-reducible graphs is their unique tree representation up to iso...

We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the np n+O(1) generator-enumeration algorithm. In previous work with Fabian Wagner, we showed an n logp n+O(logn/ log logn) time algorithm for testing isomorphism of p-groups by building graphs with degree bounded by p + O(1) that r...

We study the complexity of the Graph Isomorphism problem on graph classes that are characterized by a finite number of forbidden induced subgraphs, focusing mostly on the case of two forbidden subgraphs. We show hardness results and develop techniques for the structural analysis of such graph classes, which applied to the case of two forbidden subgraphs give the following results: A dichotomy i...