Planar

Not every planar directed acyclic graph is upward planar, and it is NP-complete to test whether a given graph is upward planar.

A 1-planar graph is a graph that may be drawn in the plane with at most one simple crossing per edge, and a k-planar graph is a graph that may be drawn with at most k simple crossings per edge.

Additionally, subdividing a graph cannot turn a nonplanar graph into a planar graph: if a subdivision of a graph G has a planar drawing, the paths of the subdivision form curves that may be used to represent the edges of G itself.

A planar graph may be drawn convexly if and only if it is a subdivision of a 3-vertex-connected planar graph.

A planar source radiates sound uniformly for low frequencies' wavelengths longer than the dimensions of the planar source, and as frequency increases, the sound from such a source focuses into an increasingly narrower angle.

A simple graph is called maximal planar if it is planar but adding any edge (on the given vertex set) would destroy that property.

Every outerplanar graph is planar, but the converse is not true: K 4 is planar but not outerplanar.

For instance, Sunúz contains terms to describe movement in a six dimensional multi-planar space, something of use to beings who visit the other planar realms where "demons" live.

Note that these theorems provide necessary conditions for planarity that are not sufficient conditions, and therefore can only be used to prove a graph is not planar, not that it is planar.

Other related families An apex graph is a graph that may be made planar by the removal of one vertex, and a k-apex graph is a graph that may be made planar by the removal of at most k vertices.

The stronger a protein's interaction with DNA, the higher the salt concentration needed to elute that protein. citation Planar chromatography Planar chromatography is a separation technique in which the stationary phase is present as or on a plane.

I don't know for us if it will be as great the transition from planar to 3D NAND was.

Owing to the flexible modulation of EM wave, metasurfaces have spawned a number of enchanting applications, such as perfect absorbers, cloaking devices, planar meta-lens and meta-hologram.

They provide tri-planar activity, activating joint stabilizers and core muscles.

Though I have yet to hear a MEMS driver for myself, xMEMS says they possess a variety of advantages over existing driver technologies like dynamic, balanced armature, and planar magnetic.

Both Planar Ornaments are rumored to be released with Version 2.1, currently expected for March 27.

Planar chips can only get bigger if you make them wider, but the ability to make chips that increase their capacity in three dimensions instead of two means the technology is much easier to scale.

The midrange vocal area and higher frequencies are where the planar magnetic drivers come into their own.

Planar chiral macrocycles have already been known to act as antibiotics and anticancer agents.

Planar scions generally change the type to outsider and gain the native subtype.