crossing number

crossing number
The minimum, taken over all planar representations of a link or graph, of the number of times it crosses itself.

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  • Crossing number — may refer to: Crossing number (knot theory) of a knot is the minimal number of crossings in any knot diagram for the knot. The average crossing number is a variant of crossing number obtained from a three dimensional embedding of a knot by… …   Wikipedia

  • Crossing number (graph theory) — A drawing of the Heawood graph with three crossings. This is the minimum number of crossings among all drawings of this graph, so the graph has crossing number cr(G) = 3. In graph theory, the crossing number cr(G) of a graph G is the… …   Wikipedia

  • 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. By way of example, the unknot has crossing number zero, the trefoil knot three and the… …   Wikipedia

  • 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… …   Wikipedia

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