The bridge number of a given knot diagram K is denoted with b(K) and refers to the minimum number of bridges possible for that knot. A bridge is considered to be an arc, a piece of a knot diagram between two undercrossings with no undercrossings in between, with at least one overcrossing. The image below represents one bridge with two overcrossings.

Curiously, the bridge number of an isotopic class is not necessarily realized in the minimal diagram for that class. For instance, the crossing number of the trefoil knot is 3, and the usual knot diagram for the trefoil has three bridges. The image below, however, reveals a trefoil with four crossings but only two bridges. Therefore, the bridging number of the trefoil knot is 2.

It is common practice to consider b(U) = 1, where U represents the unknot. Conveniently, it has been proven that, in order for a knot diagram K to represent a non-trivial curve, b(K) > 1.