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Synopsis Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to… (More)

It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required. A possibly 'intermediate' variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length… (More)

Let (E, A) be a set system consisting of a finite collection A of subsets of a ground set E, and suppose that we have a function φ which maps A into some set S. Now removing a subset K from E gives a restriction A(¯ K) to those sets of A disjoint from K, and we have a corresponding restriction φ| A(¯ K) of our function φ. If the removal of K does not affect… (More)

- A L Baker, J M Bieman, N Fenton, D A Gustafson, A C Melton, R Whitty
- 2007

Research Summary This section is intended to outline the aims and scope of this research, and the work which has already been completed. The section concludes with a proposed timetable for the remaining project. Specialised terms will be defined in the main introduction. Research Aims The aim of this research is to develop an object-oriented model for a… (More)

- Albrecht, Gaffney, A J Albrecht, J E Gaffney, Arthur, L J Arthur +16 others
- 1995

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