An approach for the recognition of polymorphic patterns by subgraph isomorphism computation of parameterized graphs will be presented. Parameterized graphs (short: p-graphs) are extensions of undirected graphs by parameter vectors at the nodes and edges. We will deene p-graphs and basic concepts of subgraph isomor-phism computation for p-graphs. A bottom-up algorithm for p-subgraph isomorphism ...

Graphs are a powerful concept useful for various tasks in science and engineering. In applications such as pattern recognition and information retrieval, object similarity is an important issue. If graphs are used for object representation, then the problem of determining the similarity of objects turns into the problem of graph matching. Some of the most common graph matching paradigms include...

We explore ways to concisely describe circulant graphs, highly symmetric graphs with properties that are easier to generalize than other graphs. We introduce connection sets as a way to describe isomorphism among some circulant graphs and discuss Ádám’s conjecture that attempts to generalize this idea to all circulant graphs, exploring cases in which the conjecture holds and cases in which it f...

It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many pairs of graphs, but the pairs of non-isomorphic graphs constructed by Cai, Fürer and Immerman it cannot distinguish. If d is fixed, then the WL-algorithm run...

Matrix symmetrization and several related problems have an extensive literature, with a recurring ambiguity regarding their complexity status and their relation to graph isomorphism. We present a short survey of these problems to clarify their status. In particular we recall results from the literature showing that matrix symmetrization is in fact NP-hard, while graph isomorphism is still an op...

Let C be any class of graphs. A graph G is C-ultrahomogeneous if every isomorphism between induced subgraphs belonging to C extends to an automorphism of G. We study graphs that are K∗-ultrahomogeneous, where K∗ is the class of complete graphs. We also explicitly classify the graphs that are tK∗-ultrahomogeneous, where tK∗ is the class of disjoint unions of complete graphs.

We consider three computational problems with unknown complexity status: The graph isomorphism problem, the problem of computing van der Waerden numbers and the problem of computing Ramsey numbers. For each of the problems, we devise an algorithm that we analyze with theoretical and practical means by a comparison with contemporary algorithms that solve the respective problems. The ScrewBox alg...

For a graph G, we are interested in a minimum-size subgraph of G which, along with an unlabelled copy of G, provides enough information to reconstruct G. We perform a preliminary study of such subgraphs, focusing on the cases where G is a complete tree or a grid. c © 2002 Elsevier Science B.V. All rights reserved.