Crossing number
Encyclopedia
Crossing number may refer to:
- Crossing number (knot theory)Crossing number (knot theory)In the mathematical area of knot theory, the crossing number of a knot is the minimal number of crossings of any diagram of the knot. It is a knot invariant....
of a knot is the minimal number of crossings in any knot diagram for the knot.- The average crossing numberAverage crossing numberIn the mathematical subject of knot theory, the average crossing number of a knot is the result of averaging over all directions the number of crossings in a knot diagram of the knot obtained by projection onto the plane orthogonal to the direction...
is a variant of crossing number obtained from a three-dimensional embedding of a knot by averaging over all two-dimensional projections.
- The average crossing number
- Crossing number (graph theory)Crossing number (graph theory)In graph theory, the crossing number cr of a graph G is the lowest number of edge crossings of a planar drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero.The concept originated in...
of a graph is the minimal number of edge intersections in any planar representation of the graph.