Tait's Flyping Conjecture for 4-Regular Graphs

1998/06/22 by J. Sawollek, Sawollek, J.
Mathematics · #57M15 #57M25 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:57M15 #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/9806119

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

arxiv created 2005/05/11 · arxiv updated 2009/11/30

Abstract

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 S³. 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.

Related

• A geometric proof of the flyping theorem
• The Tait conjecture in S¹xS²
• The Tait conjecture in g(S¹xS²)
• Polynomial algorithm for alternating link equivalence
• The virtual flyping theorem