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 number
      Average crossing number
      In 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.
  • 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.
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