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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 lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero. Determining the ...
A zero-crossing in a line graph of a waveform representing voltage over time. A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function.
It states that, for graphs where the number e of edges is sufficiently larger than the number n of vertices, the crossing number is at least proportional to e 3 /n 2. It has applications in VLSI design and combinatorial geometry, and was discovered independently by Ajtai, Chvátal, Newborn, and Szemerédi [1] and by Leighton. [2]
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 averaging over all two-dimensional projections. The link crossing number is the sum of ...
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[1] [2] Planarization may be performed by using any method to find a drawing (with crossings) for the given graph, and then replacing each crossing point by a new artificial vertex, causing each crossed edge to be subdivided into a path. The original graph will be represented as an immersion minor of its planarization.
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A 23-year-old hiker who survived 13 days lost in the Australian wilderness after stumbling on two granola bars has thanked his rescuers for enduring “tough conditions” to find him.