  We study embeddings of the $n$-dimensional hypercube into the circuit with
$2^n$ vertices. We prove that the circular wirelength attains minimum by gray
coding, which is 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 doctor dissertation "The circular wirelength problem for hypercubes"
(University of California, Riverside, 1997). Many people argue there are gaps
in her proof. We eliminate gaps in her dissertation.

Combinatorics