The subgraph isomorphism problem involves deciding if there exists a copy of a pattern graph in a target graph. This problem may be solved by a complete tree search combined with filtering techniques that aim at pruning branches that do not contain solutions. We introduce a new filtering algorithm based on local all different constraints. We show that this filtering is stronger than other exist...

Comparability graphs are graphs which have transitive orientations. The dimension of a poset is the least number of linear orders whose intersection gives this poset. The dimension dim(X) of a comparability graph X is the dimension of any transitive orientation of X, and by k-DIM we denote the class of comparability graphs X with dim(X) ≤ k. It is known that the complements of comparability gra...

Algorithms for finding frequent and/or interesting subgraphs in a single large graph scenario are computationally intensive because of the graph isomorphism and the subgraph isomorphism problem. These problems are compounded by the size of most real-world datasets which have sizes in the order of 10 or 10. The SUBDUE algorithm developed by Cook and Holder finds the most compressing subgraph in ...

We study the isomorphism problem of two “natural” algebraic structures – F-algebras and cubic forms. We prove that the F-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form 3 6 |(#F − 1), this result implies that the two problems are infact equivalent. This result also has the follo...

Mumford defined a natural isomorphism between the intermediate jacobian of a conicbundle over P and the Prym variety of a naturally defined étale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used this isomorphism to give a proof of the irrationality of a smooth cubic threefold and Beauville later generalized the isomorphism to intermediate jacobians of odd-di...

If Tψ is an ergodic group extension of a weakly mixing transformation T having minimal self-joinings, then it is shown that isomorphism between Tψ and its inverse implies isomorphism between T and T−1. However, if T satisfies the weaker condition of being simple it is shown that that isomorphism between Tψ and its inverse does not imply the isomorphism between T and T−1. This answers a question...

We say that a degree is low for isomorphism if, whenever it can compute an isomorphism between a pair of computable structures, there is already a computable isomorphism between them. We show that while there is no clear-cut relationship between this property and other properties related to computational weakness, the low-forisomorphism degrees contain all Cohen 2-generics and are disjoint from...

We consider the algebra isomorphism found by Frenkel and Ding between the RLL and the Drinfeld realizations of Uq(ĝl(2)). After we note that this is not a Hopf algebra isomorphism, we prove that there is a unique Hopf algebra structure for the Drinfeld realization so that this isomorphism becomes a Hopf algebra isomorphism. Though more complicated, this Hopf algebra structure is also closed, ju...