The biwheel conjecture asserts that the minimum number 
of perfect matchings
in a simple brace graph on 
vertices satisfies
 |
for every sufficiently large even integer 
(Feng and Zhou 2026). Trapezohedral
graphs, also called biwheels, attain this value.
Feng and Zhou (2026) proved the conjecture. The restriction to sufficiently large even order is essential, since small brace graphs can have fewer perfect matchings than the corresponding trapezohedral graph.
