2018/01/25 by Wendy Myrvold, Jennifer Woodcock · 2 citations
Computer Science · Engineering · Mathematics · #Digital and Cyber Forensics #Integrated Circuits and Semiconductor Failure Analysis #Mechanical stress and fatigue analysis #Torus #Embedding #Mathematics #Set (abstract data type) #Planar graph #Graph #Book embedding #Quadratic equation #Graph embedding #Combinatorics #Discrete mathematics #Algorithm #Theoretical computer science #1-planar graph #Computer science #Chordal graph #Artificial intelligence #Geometry
paper · pdf · doi:10.37236/3797
openalex publication_date 2018/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
We outline the progress made so far on the search for the complete set of torus obstructions and also consider practical algorithms for torus embedding and their implementations. We present the set of obstructions that are known to-date and give a brief history of how these graphs were found. We also describe a nice algorithm for embedding graphs on the torus which we used to verify previous results and add to the set of torus obstructions. Although it is still exponential in the order of the graph, the algorithm presented here is relatively simple to describe and implement and fast-in-practice for small graphs.It parallels the popular quadratic planar embedding algorithm of Demoucron, Malgrange, and Pertuiset.