Tait's Flyping Conjecture for 4-Regular Graphs

Details Tait's Flyping Conjecture for 4-Regular Graphs Tait's Flyping Conjecture for 4-Regular Graphs

1998-06-22

arxiv.org/abs/math/9806119v2

Mathematics

Geometric Topology

20 pages, 13 figures, latex2e, metafont; main theorem generalized (without condition "vertex-separating"), to appear in JCTB

Scientific paper

Tait's flyping conjecture, stating that two reduced, alternating, prime link diagrams can be connected by a finite sequence of flypes, is extended to reduced, alternating, prime diagrams of 4-regular graphs in S^3. The proof of this version of the flyping conjecture is based on the fact that the equivalence classes with respect to ambient isotopy and rigid vertex isotopy of graph embeddings are identical on the class of diagrams considered.

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