Lennart Rudolph

Simpler Graph Conditions for Embedding Tetrahedral Meshes

Three-dimensional Tutte-style embedding methods turn graph conditions into guarantees for tetrahedral meshes. Alexa's theorem excludes both K_6 and K_(3,3,1) as graph minors and asks whether the second exclusion is necessary. We prove that it is redundant for a precisely defined...

Exact Projection Quality of OneTwo Sobol' Sequences at 65,536 Points

Low-dimensional projection quality is a practical bottleneck for Sobol' sequences used in quasi-Monte Carlo integration and computer graphics. For a digital net with 2^16 = 65,536 points, the t-value measures exact equidistribution in dyadic boxes, with smaller values indicating...

An Infinite Dense Counterexample Family for Extremal First Betti Numbers of Flag Complexes

Beers and Bakke Botnan conjectured that every graph maximizing the first reduced Betti number of its flag complex among graphs with fixed numbers of vertices and edges contains a complete bipartite spanning subgraph. We give an infinite family of counterexamples strictly above th...