Examples of 'crossing number' in a sentence
Meaning of "crossing number"
crossing number ~ a mathematical term used to describe the minimum number of crossings that occur when lines or curves in a graph are drawn without lifting the pen
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- The minimum, taken over all planar representations of a link or graph, of the number of times it crosses itself.
How to use "crossing number" in a sentence
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crossing number
It is known as the crossing number inequality or crossing lemma.
The notation simply organizes knots by their crossing number.
Asymptotic crossing number is conjectured to be equal to crossing number.
Both of these quantities bound the standard crossing number.
The crossing number inequality.
Prime knots are organized by the crossing number invariant.
No knots with crossing number smaller than twelve are positive amphichiral.
The number of variations increases exponentially with the crossing number.
There are related concepts of average crossing number and asymptotic crossing number.
The crossing number is even if and only if the point is outside the polygon.
The unknotting number of a knot is always less than half of its crossing number.
The average crossing number is often seen in the context of physical knot theory.
This has come to be known as the Zarankiewicz crossing number conjecture.
Cycle crossing number was used to determine log cell concentration according to a standard curve.
A big open question asks if the crossing number is additive when taking knot sums.
See also
The crossing number of the McGee graph is 8.
Further values are collected by the Rectilinear Crossing Number project.
To obtain the actual crossing number inequality, we now use a probabilistic argument.
Traditionally, knots have been catalogued in terms of crossing number.
For a planar graph, the crossing number is zero by definition.
The crossing number of a reduced, alternating diagram is the crossing number of the knot.
These algorithms are used in the Rectilinear Crossing Number distributed computing project.
A graph with crossing number k is necessarily k-planar, but not necessarily vice versa.
In seeking from one track to another, a track crossing number is determined.
The crossing number method uses a 3 × 3 window to examine the local neighborhood of each ridge pixel.
More generally, any graph with crossing number 1 is toroidal.
Including the Heawood graph, there are 8 distinct graphs of order 14 with crossing number 3.
Many of the knots with crossing number less than 10 are alternating.
One of three non-alternating knots with crossing number 8.
The rectilinear crossing number of the Coxeter graph is 11.
Thus, the Petersen graph has crossing number 2.
Crossing Number ( knot Theory ).
The Heawood graph has crossing number 3.
There exists 5 non-isomorphic cubic graphs of order 24 with crossing number 8.
The Tietze graph has crossing number 2 and is 1-planar.
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