3 papers
math.CO2024
Stable cuts, NAC-colourings and flexible realisations of graphs
Katie Clinch, Dániel Garamvölgyi, John Haslegrave +3
A (2-dimensional) realisation of a graph is a pair , where maps the vertices of to . A realisation is flexible if it can be continuously deformed w…
cs.CG2024
Flexible realizations existence: NP-completeness on sparse graphs and algorithms
Petr Laštovička, Jan Legerský
One of the questions in Rigidity Theory is whether a realization of the vertices of a graph in the plane is flexible, namely, if it allows a continuous deformation preserving the e…
math.MG2024
Pentagonal bipyramids lead to the smallest flexible embedded polyhedron
Matteo Gallet, Georg Grasegger, Jan Legerský +1
Steffen's polyhedron was believed to have the least number of vertices among polyhedra that can flex without self-intersections. Maksimov clarified that the pentagonal bipyramid wi…