One of the main differences between ILP and graph mining is that while pattern matching in ILP is mainly defined by homomorphism (subsumption), it is the subgraph isomorphism in graph mining. Using that subgraph isomorphisms are injective homomorphisms, we bridge the gap between the two pattern matching operators with partially injective homomorphisms, which are homomorphisms requiring the inje...

Efficient zero-knowledge proofs of knowledge for homomorphisms are a key building block in a vast number of constructions in applied cryptography. Examples are: identification-, signature-, group signature-, anonymous credential-, and identity escrow-schemes as well as voting systems, e-cash, multi-party computations, and trusted computing. This dissertation studies efficient zero-knowledge pro...

Let hom(G,H) denote the number of homomorphisms from a graph G to a graph H. In this paper we study the number of homomorphisms of trees into a path, and prove that hom(Pm, Pn) ≤ hom(Tm, Pn) ≤ hom(Sm, Pn), where Tm is any tree on m vertices, and Pm and Sm denote the path and star on m vertices, respectively. This completes the study of extremal problems concerning the number of homomorphisms be...

We demonstrate that categories of continuous actions topological monoids on discrete spaces are Grothendieck toposes. exhibit properties these toposes, giving a solution to the corresponding Morita-equivalence problem. characterize toposes in terms their canonical points. identify natural classes representatives with good properties, 'powder monoids' and then 'complete monoids', for monoids. Fi...

Rick Brewster, Thompson Rivers University Graph Homomorphisms, an introduction This talk is an introduction to the subject of graph homomorphisms. The concept of homomorphisms appears in many areas of mathematics, and the field of graph theory is no exception. However, until recently most graph theorists did not view graph homomorphisms as a central topic in the discipline. In their recent book...

This paper investigates function spaces of partially ordered sets with some directed family of projections. Given a xed directed index set (I;), we consider triples (D; ; (p i) i2I) consisting of a poset (D;) and a monotone net (p i) i2I of projections of D. We call them (I;)-indexed pop's (posets with projections). Our main purpose is to study structure preserving maps between (I;)-indexed pop...