14 papers · 1 filter
The minimum degree question for the Maker Breaker Domination Game
Jakob Führer, Georg Grasegger, Paul Hametner +1
The Maker Breaker Domination Game is a two player game played on a graph in which the players take turns to claim a vertex from the graph. The aim of the Dominator is to claim…
Counting fibres of the Hadamard product using Bergman fans
Oliver Clarke, Sean Dewar, Matteo Gallet +3
We study the generic fibre of the Hadamard product of linear spaces via matroid theory and tropical geometry. To do so, we introduce the flip product, a numerical invariant associa…
Computing the number of realisations of a rigid graph
Sean Dewar, Georg Grasegger, Josef Schicho +2
A graph is said to be rigid if, given a generic realisation of the graph as a bar-and-joint framework in the plane, there exist only finitely many other realisations of the graph w…
Explorations on the number of realizations of minimally rigid graphs
Georg Grasegger
Rigid graphs have only finitely many realizations. In the recent years significant progress was made in computing the number of such realizations. With this progress it was also po…
Constructing reflection-symmetric flexible realisations of graphs
Sean Dewar, Georg Grasegger, Jan Legerský
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessa…
Angular constraints on planar frameworks
Sean Dewar, Georg Grasegger, Anthony Nixon +4
Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of directi…