A Rigorous Proof on Circular Wirelength for Hypercubes

We study embeddings of the n-dimensional hypercube into the circuit with 2ⁿ vertices. We prove that the circular wirelength attains a minimum by gray coding; that was called the CT conjecture by Chavez and Trapp (Discrete Applied Mathematics, 1998). This problem had claimed to be settled by Ching-Jung Guu in her doctoral dissertation “The circular wirelength problem for hypercubes” (University of California, Riverside, 1997). Many argue there are gaps in her proof. We eliminate the gaps in her dissertation. [Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.][Figure not available: see fulltext.].