A brace graph, usually called a brace, is a connected graph that is bipartite, has at least one edge, and is matching covered, with no nontrivial tight edge cut. Matching covered means that every edge belongs to a perfect matching. A tight edge cut meets every perfect matching in exactly one edge, and it is nontrivial when both sides contain more than one vertex (Feng and Zhou 2026). Braces are the bipartite graph building blocks of tight-cut decomposition.
The biwheel conjecture determines the minimum number of perfect matchings in simple brace graphs of sufficiently large even order.
