Combining the the results of A.R. Meyer and L.J. Stockmeyer " The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space " , and K.S. Booth " Iso-morphism testing for graphs, semigroups, and finite automata are polynomiamlly equivalent problems " shows that graph isomorphism is PSPACE-complete. The equivalence problem for regular expressions was shown to be PSPACE-...

We study a graph transformation (defined by Seidel) called switching which, given a graph G = ( V,E) and a subset W C Jf of its vertices, builds a new graph by exchanging the cocycle linking W to V\ W with its complement. Switching is an equivalence relation and the associated equivalence classes are called switching classes. A switching class is perfect if it contains only perfect graphs. We s...

Given an (un)directed connected graph G = (V; E) as a set of edges, let ?(v) be the set of neighbors of a vertex v 2 V. We show that the equivalence-relation R with uRv :, ?(u) = ?(v) on the vertices of the graph can be computed in linear time and space. Many problems can be solved on the graph G induced by the equivalence-classes and the result extended to G. An example for this is the all-pai...

We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. By constructing a graph on ribbon tableaux which we transform into a dual equivalence graph, we give a combinatorial proof of the symmetry and Schur positivity of the ribbon tableaux generating func...

Indiana University and the University of Washington 2Chain graphs (CG) (= adicyclic graphs) use undirected and directed edges to represent simultaneously both structural and associative dependences.. Like acyclic directed graphs (ADGs), the CG associated with a given statistical model may not be unique, so CGs fall into Markov equivalence classes, which may be superexponentially large, leading ...

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, if P(G) = P(H). A set of graphs S is called a chromatic equivalence class if for any graph H that is chromatically equivalent with a graph G in S, then H ∈S. Peng et al. (Discrete Math. 172 (1997) 103–114), studied the chromatic equivalence classes of certain generalized polygon trees. In thi...

We present a new method for representating the state spaces of hierarchical level of detail descriptions, or scene descriptions with multiple hierarchical levels of detail. This representation, called a level of detail graph, permits the investigation and exploration of the state spaces of non-hierarchical and hierarchical level of detail optimization algorithms. We present algorithms for gener...

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1, . . . , m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K2 has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomp...

We make a systematic study of a new combinatorial construction called a dual equivalence graph. Motivated by the dual equivalence relation on standard Young tableaux introduced by Haiman, we axiomatize such constructions and prove that the generating functions of these graphs are Schur positive. We construct a graph on k-ribbon tableaux which we conjecture to be a dual equivalence graph, and we...