Theorem provers were also called ’proof checkers’ because that is what they were in the beginning. They have grown powerful, however, capable in many cases to automatically produce complicated proofs. In particular, higher order logic based theorem provers such as HOL and PVS became popular because the logic is well known and very expressive. They are generally considered to be potential platfo...

We prove a generalization of a theorem of Ganter concerning the embedding of partial Steiner systems into Steiner systems. As an application we discuss a further version of the problem of Rosenfeld on embedding graphs into strongly regular graphs.

Kenneth Kunen showed that there is no non-trivial elementary embedding of the universe V into itself.We generalize this theorem by proving that there is no non-trivialgeneric elementary embedding of V into itself.

2 Embedding graphs into planarity 3 2.1 embedding algorithms donot use PQ-trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 A planarity embedding algorithm based on the Kuratowski theorem . . . . . . . . 3 2.1.2 An embedding algorithm based on open ear decomposition . . . . . . . . . . . . . . 3 2.1.3 A simplified o (n) planar embedding algorithm for biconnected graphs . . ....

In this paper, we consider the problem of embedding formal notations. In particular, we describe our experiences of automating the embedding of Z speciications into the notations of the PVS and HOL theorem provers. This paper is motivated by our experiences of constructing a prototype tool for embedding formal notations and its use in automating an embedding of Z and AMN into the notations of P...

This paper is concerned with applications of Tutte’s barycentric embedding theorem (1963, Proc. London Math. Soc. 13, 743–768). It presents a method for building isotopies of triangulations in the plane, based on Tutte’s theorem and the computation of equilibrium stresses of graphs by Maxwell–Cremona’s theorem; it also provides a counterexample showing that the analogue of Tutte’s theorem in di...

We describe how some simple properties of discrete one-forms directly relate to some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte’s celebrated “springembedding” theorem for planar graphs, which is widely used for parameterizing meshes with the topology of a disk as a planar embedding with a convex boundary. Our second result gen...