43 citations · 82 across the 12 of their papers we have counts for
6 papers · 1 filter
Radically solvable graphs
Bill Jackson, J. C. Owen
A 2-dimensional framework is a straight line realisation of a graph in the Euclidean plane. It is radically solvable if the set of vertex coordinates is contained in a radical exte…
The number of equivalent realisations of a rigid graph
Bill Jackson, J. C. Owen
Given a rigid realisation of a graph in , it is an open problem to determine the maximum number of pairwise non-congruent realisations which have the same edge l…
An Inductive Construction of (2,1)-tight Graphs
Anthony Nixon, John Owen
The simple graphs that satisfy for any subgraph (and for ) are the -sparse graphs. Those that also satisfy are the …
Rigidity of Frameworks Supported on Surfaces
A. Nixon, J. C. Owen, S. C. Power
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory…
Distance Configurations of Points in a Plane with a Galois group that is not Soluble
John C. Owen, Stephen C. Power
We have conjectured that the constraint equations defined by a generic Laman graph are not soluble by radicals when the graph is 3-connected. We prove that this conjecture follows…
Generic 3-connected planar constraint systems are not soluble by radicals
John C. Owen, Stephen C. Power
We show that planar embeddable 3-connected CAD graphs are generically non-soluble. A CAD graph represents a configuration of points on the Euclidean plane with just enough distance…