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A large set of torus obstructions and how they were discovered. (English) Zbl 1380.05134
Summary: 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 G. Demoucron et al. [Rev. Franç. Rech. Opér. 8, No. 30, 33–47 (1964; Zbl 0128.17203)].

05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C83 Graph minors
05C10 Planar graphs; geometric and topological aspects of graph theory
05C85 Graph algorithms (graph-theoretic aspects)
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