2 citations · 5 across the 5 of their papers we have counts for
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Kalai's conjecture for unconditional and locally anti-blocking polytopes
Raman Sanyal, Martin Winter
Kalai's conjecture states that every centrally-symmetric -polytope has at least faces. We give short proofs for two special cases: if is unconditional (that is,…
The clique graphs of the hexagonal lattice -- an explicit construction and a short proof of divergence
Martin Winter
We present a new, explicit and very geometric construction for the iterated clique graphs of the hexagonal lattice which makes apparent its clique-divergence and she…
Characterising Clique Convergence for Locally Cyclic Graphs of Minimum Degree
Anna M. Limbach, Martin Winter
The clique graph of a graph has as its vertices the cliques (maximal complete subgraphs) of , two of which are adjacent in if they have non-empty intersection in $…
Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints
Martin Winter
We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interio…
Symmetric and Spectral Realizations of Highly Symmetric Graphs
Martin Winter
A realization of a graph is a map that assigns to each vertex a point in -dimensional Euclidean space. We study graph realizations from the pers…
Vertex-Facet Assignments For Polytopes
Thomas Jahn, Martin Winter
Motivated by the search for reduced polytopes, we consider the following question: For which polytopes exists a vertex-facet assignment, that is, a matching between vertices and no…