- Publications
- Influence

Claim Your Author Page

Ensure your research is discoverable on Semantic Scholar. Claiming your author page allows you to personalize the information displayed and manage publications.

Chaotic dynamical systems have received a great deal of attention in recent years (see for instance [2], [3]). Although there has been no universally accepted mathematical definition of chaos, the… (More)

- Grant Cairns, Yury Nikolayevsky
- Discrete & Computational Geometry
- 2000

Abstract. A thrackle (resp. generalized thrackle) is a drawing of a graph in which each pair of edges meets precisely once (resp. an odd number of times). For a graph with n vertices and m edges, we… (More)

- Grant Cairns, Yury Nikolayevsky
- Discrete & Computational Geometry
- 2009

A graph drawing is called a generalized thrackle if every pair of edges meets an odd number of times. In a previous paper, we showed that a bipartite graph G can be drawn as a generalized thrackle on… (More)

C.F. Gauss gave a necessary condition for a word to be the intersection word of a closed normal planar curve and he gave an example which showed that his condition was not sufficient. M. Dehn… (More)

We give a new formula for the winding number of smooth planar curves and show how this can be generalized to curves on closed orientable surfaces. This gives a geometric interpretation of the notion… (More)

C.F. Gauss gave a necessary condition for a word to be the intersection sequence of a closed normal planar curve and he gave an example which showed that his condition was not sufficient. Since then… (More)

Computer-aided theorem-proving has been the object of recent research in China. The pioneering work of Wu Wentsun [5] described an algebraic algorithm that was successful in proving nontrivial… (More)

An action of a group, G, on a space, M, is chaotic if it is topologically transitive and the set of points with finite orbit is a dense subset of M. In this paper we show that every compact… (More)

- Grant Cairns, Stacey Mendan
- Ars Math. Contemp.
- 2013

We give an improvement of a result of Zverovich and Zverovich which gives a condition on the first and last elements in a decreasing sequence of positive integers for the sequence to be graphic, that… (More)