Glossary of graph theory

This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by edges.

!$@

A

B

C

D

E

F

G

H

I

K

κ(G) is the size of the maximum clique in G; see clique.

L

M

N

O

P

Q

R

S

T

U

V

W

References

Trail (horse show)

Trail is a competitive class at horse shows where horses and riders in western-style attire and horse tack navigate a series of obstacles. Contestants ride the course one at a time. Originally designed to resemble situations a horse and rider might actually encounter when on a trail in a natural habitat, modern trail classes now tend to focus more heavily on agility and manners, with courses bearing very little resemblance to real-world natural trails.

A typical trail course requires horse and rider to open and pass through a small gate while mounted; walk across a fake bridge; cross over a set of rails or logs at a walk, trot or lope; back up, often with a turn while backing; sidepass, often over a rail or log; turn on the forehand or hindquarters within a confined area; and tolerate some type of "spooky" obstacle, such as having the rider put on a vinyl raincoat. The horse is asked to perform all three gaits in the process of completing the course.

Additional obstacles or tests may include walking over a plastic tarp or through water; having the horse ground-tie (remain standing in one spot while the rider walks away); to walk, trot or lope in very tight quarters, such as traveling through a series of cones or markers in a serpentine pattern; or take a small jump (usually under 18 inches, as riders are in western saddles and cannot easily get off the horse's back into a jumping position).

400 Trail

The 400 Bike Trail is a 22-mile (35 km) rail trail between Reedsburg and Elroy, Wisconsin. It is designed for foot, bicycle, equestrian, snowmobile traffic. It is designated as a multiuse trail, offering recreational access to the routes, and is open to the public.

It is one of four connecting bike trails in west-central Wisconsin that spans approximately one-third of the state. The trail is known for its rural scenery of the Baraboo River which it crosses eleven times. It is part of the larger Wisconsin bike trail system, operated by the state of Wisconsin.

The four connecting west central Wisconsin trails, known as the Bike 4 Trails, going from southeast to northwest are:

The 400 trail connects to the Elroy-Sparta State Trail in Elroy.

The trail headquarters is located in a historic depot in Reedsburg and is open from May 1 through October 31. There is a $4.00 per day fee for use of the trail if one does not have the $20.00 yearly Wisconsin bike trail pass. Bike lights are advisable even on the brightest summer days when going into the long unlit tunnels. Camping, lodging, food, parking, bike rentals and information are available at many points along the trail.

Mix

Mix, mixes, mixture, or mixing may refer to:

In mathematics, science, and technology

In electronics and telecommunications

Other uses in mathematics, science, and technology

DJ mix

A DJ mix or DJ mixset is a sequence of musical tracks typically mixed together to appear as one continuous track. DJ mixes are usually performed using a DJ mixer and multiple sounds sources, such as turntables, CD players, digital audio players or computer sound cards, sometimes with the addition of samplers and effects units, although it's possible to create one using sound editing software.

DJ mixing is significantly different from live sound mixing. Remix services were offered beginning in the late 1970s in order to provide music which was more easily beatmixed by DJs for the dancefloor. One of the earliest DJs to refine their mixing skills was DJ Kool Herc.Francis Grasso was the first DJ to use headphones and a basic form of mixing at the New York nightclub Sanctuary. Upon its release in 2000, Paul Oakenfold's Perfecto Presents: Another World became the biggest selling dj mix album in the US.

Music

A DJ mix is often put together with music from genres that fit into the more general term electronic dance music. Other genres mixed by DJ includes hip hop, breakbeat and disco. Four on the floor disco beats can be used to create seamless mixes so as to keep dancers locked to the dancefloor. Two of main characteristics of music used in dj mixes is a dominant bassline and repetitive beats. Music mixed by djs usually has a tempo which ranges from 120 bpm up to 160 bpm.

Audio mixing

Audio mixing is the process by which multiple sounds are combined into one or more channels. In the process, the source signals' level, frequency content, dynamics, and panoramic position are manipulated and effects such as reverb may be added. This practical, aesthetic, or otherwise creative treatment is done in order to produce a mix that is more appealing to listeners.

Audio mixing is practiced for music, film, television and live sound. The process is generally carried out by a mixing engineer operating a mixing console or digital audio workstation.

Recorded music

Before the introduction of multitrack recording, all the sounds and effects that were to be part of a recording were mixed together at one time during a live performance. If the mix wasn't satisfactory, or if one musician made a mistake, the selection had to be performed over until the desired balance and performance was obtained. However, with the introduction of multitrack recording, the production phase of a modern recording has radically changed into one that generally involves three stages: recording, overdubbing, and mixdown.