2 research outputs found
Jungerman ladders and index 2 constructions for genus embeddings of dense regular graphs
We construct several families of genus embeddings of near-complete graphs
using index 2 current graphs. In particular, we give the first known minimum
genus embeddings of certain families of octahedral graphs, solving a
longstanding conjecture of Jungerman and Ringel, and Hamiltonian cycle
complements, making partial progress on a problem of White. Index 2 current
graphs are also applied to various cases of the Map Color Theorem, in some
cases yielding significantly simpler solutions, e.g., the nonorientable genus
of . We give a complete description of the method, originally
due to Jungerman, from which all these results were obtained.Comment: 23 pages, 21 figures; fixed 2 figures from previous versio