In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two adjacent edges have the same color.
 For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green.
 Edge colorings are one of several different types of graph coloring.
 The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most k different colors, for a given value of k , or with the fewest possible colors.
 The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph.
 For example, the edges of the graph in the illustration can be colored by three colors but cannot be colored by two colors, so the graph shown has chromatic index three.
Zero is an even number.
 In other words, its "parity"—the quality of an integer being even or odd—is even.
 The simplest way to prove that zero is even is to check that it fits the definition of "even": it is an integer multiple of 2, specifically 0 × 2 .
 As a result, zero shares all the properties that characterize even numbers: 0 is divisible by 2, 0 is neighbored on both sides by odd numbers, 0 is the sum of an integer (0) with itself, and a set of 0 objects can be split into two equal sets.
The Gibson Victory was an electric guitar produced by Gibson Guitars from 1981 until 1983 (although some sources say production lasted until 1984).
 During the late 1970s and early 1980s, musicians watched Eddie Van Halen play his Frankenstrat and questioned and rethought everything about their instruments.
 They insisted on engineering advances allowing more speed and playability of skyscraping leads and rock crushing shred.
 The master luthiers in Kalamazoo responded to these demanding guitarists by designing the Victory.
 The Victory, a superstrat, was radical departure from Gibson's image as an old-fashioned guitar maker.
 MV stood for Multi-Voice.
 X stood for ten They were created by the Gibson research and development team in Kalamazoo, MI, with the body work by Chuck Burge, and the multi-voice electronics by Tim Shaw.
 The Victory MV's were available with an optional / special order Kahler Tremolo System.
 The Victory MV's had the first three-point top-adjust bridge designed by Rendal Wall and patent granted in June 1982.
 The three post holes in the underside allowed either side of the bridge unit to be moved forwards or backwards allowing intonation of ultra light to extremely heavy string gauges, and twelve interchangeable individually-adjustable saddles, six standard nylon saddles and 6 optional brass saddles for fine adjustment of intonation and to affect tone.
 String gauge affects sound and playability.
 If you are a professional with strong fingers, using heavier strings produces greater dynamic and timbral range, more sustain, & less buzzing using slide.
 Using lighter strings allows easier bending, easier hammer-ons, pull-offs & very fast solos.
 Victories were built tough and stiff to easily handle the high tension of using much heavier string gauges without a truss rod adjustment.
 The Victory MV's came with a series of specially designed Humbucker Pickups carefully made one at a time on the “center focused” KZ/LP115 PAF Pickup Winder, with high sensitivity and unique tonal signature with fewer turns of wire compared to newer high production winding machines that produce more scatter and a wider magnetic aperture, Each pickup across the range is different, and specifically designed for the role it was assigned.
 Most musicians adjust the height of the individual pole pieces so they mirror the radius of the fretboard and then fine adjust by ear.
 The location of the Victory MV's pickups were carefully calculated to provide full frequency response and minimize dead spots by avoidance of string nodal points.
 The majority of harmonics coincide with where the twenty fourth fret would be located.
 If you want to play your Victory above the 22nd fret, use a ring slide.
 Humbucker pickups are inherently low noise because the interference is significantly reduced via phase cancellation, however the Victory MV’s have additional shielding connected to ground with the use of special electrically conductive black paint in the routed out area under the pickguard.
 Truly silent when it should be.
 The coil tap switch in the up position is humbucker; in the down position is single coil, indistinguishable from traditional unshielded single coils minus the noise.
 Victory MV’s are totally immune from “Strat-Itis” (simultaneous multiple discordant frequency syndrome) In other single-coil pickups, strat-Itis is an annoying out-of-tune harmonic, oscillating/warbling /shriek/dissonant sound.
 Gibson had well established business agreements for over 100 years with the best wood suppliers in the world and Gibson Luthiers had first pick to craft the Victory MV's.
 The availability of premium old growth wood with tight grain was better in the 1980s than it is today because of new laws and limited natural resources.
 The Victory MV's body and tri-laminated quartersawn neck were crafted from solid eastern hard rock maple, with a Janka Hardness ranking of 1450 pound-force, a crushing strength of 7,830 pound-force per square inch , and a tensile elasticity modulus of 1,830,000 pound-force per square inch.
 Eastern Hard Rock Maple is extremely hard, dense, and stiff, producing earthquaking sustain.
 The stacked laminate opposing wood grain neck design strengthens the overall neck, gives more tuning stabilization, and allowed the luthiers to eliminate the scarf joint at the headstock.
 Contrasting mirror image graining angles provide the best resistance against impact cracking over single piece or scarf joint necks.
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 Wood improves with age, the polymerization of sap over decades, once the wood is removed from the living tree crystalizes.
 Aged wood also loses its ability to absorb moisture, causing the wood to become more stiff and stable as it ages… the perfect recipe for a straight, high quality guitar neck, level fret board, and great sound.
 Victory MV’s have binding along the edges of the fretboard that cover the unfinished fret tangs and fret slot end gaps, slightly covering the nibs on the fret ends that can protrude.
  Binding is tedious painstaking work and requires skill to install properly, but provides a slick smooth feel, is especially nice for sliding your hand along the fretboard, and gives a dressy look.
 Not to be confused with undercut, fret over binding.
 Using glue that is stronger than the wood itself, the Victory MV's mortise-and-tenon Set-in neck and silky smooth rock-hard quartersawn Madagascan ebony fret board required better tools, more time, accuracy, attention to detail, and skill to craft, but produces a warmer fuller tone and transfers resonant energy freely and immediately due to the tight permanent coupling, and facilitates ripples of vibrational energy that round out and thicken the sound.
 (Unlike other guitars with weak removable "screw-on" necks with a metal plate, adjustment shims, and a creaky neck pocket / body gap.
 So called "bolt-on" necks have no proper neck torque specs, over-tightening the screws crushes the wood, cracks the finish, and strips the holes or screw head, requiring a toothpick or dowel to be glued in the stripped hole).
 The Victory's elegant headstock shape has a fourteen degree non-scarfed break angle, and tuning machine alignment that allows for a "perfectly straight" symmetrical pull on the strings that provides optimum string down pressure on the nut for the string to seat in the nut slot but not pinch, bind, or rattle in the slot, transferring all the vibration into the nut instead of into the tuning machines.
 (Unlike other guitars that need junky string tree clips, retainers, or guides that cause friction and pings/cracking noise.)
 The Victories chamfered cutaway offers musicians with large hands better access to play in the top frets.
 The Gibson Victory MV's are not recommended for the weak, these sledge axes weigh a solid nine pounds but are perfectly balanced both on the strap or on the knee, Luthiers know guitars with more mass and density have more brilliance and sustain.
 According to Gibson, Victory MV’s were only produced in Candy Apple Red, Antique Cherry Sunburst, & Twilight Blue.
 However sometimes a retailer who did a lot of business with Gibson would be able to ask for a small number of guitars with a special finish.
 Mention has been made of Roy Orbison's special order black Victory MVX.
 The Victory MV's came standard with a rugged black Gibson branded "8170" dual lock and key padded hard case with internal storage box.
 Decode the serial number on the back of the headstock to determine if your Victory was hand made by finding the location and the date of it's manufacture.
Beryllium (Be) has 12 known isotopes, but only one of these isotopes ( Be ) is stable and a primordial nuclide.
 As such, beryllium is considered a monoisotopic element.
 It is also a mononuclidic element, because its other isotopes have such short half-lives that none are primordial and their abundance is very low (standard atomic weight is 9.0122).
 Beryllium is unique as being the only monoisotopic element with both an even number of protons and an odd number of neutrons.
 There are 25 other monoisotopic elements but all have odd atomic numbers, and even numbers of neutrons.
In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number "n" such that the sum of all divisors of "n" (the sum-of-divisors function "σ"("n")) is equal to 2"n" − 1, the sum of all proper divisors of "n", "s"("n") = "σ"("n") − "n", then being equal to "n" − 1.
 The only known almost perfect numbers are powers of 2 with non-negative exponents (sequence in the OEIS) .
 Therefore the only known odd almost perfect number is 2 = 1, and the only known even almost perfect numbers are those of the form 2 for some positive number "k"; however, it has not been shown that all almost perfect numbers are of this form.
 It is known that an odd almost perfect number greater than 1 would have at least six prime factors.
The following is a list of the known perfect numbers, along with the Mersenne prime exponent "p" which generates them with the expression 2× (2 − 1) where 2 − 1 is a Mersenne prime.
 All even perfect numbers are of this form.
 It is not known whether there are any odd perfect numbers.
 s of 2016 there are 49 known perfect numbers in total.
 The ratio "p" / digits approaches log(10) / log(4) = 1.6609640474...
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
 An integer is even if it is evenly divisible by two and odd if it is not even.
 For example, 6 is even because there is no remainder when dividing it by 2.
 By contrast, 3, 5, 7, 21 leave a remainder of 1 when divided by 2.
 Examples of even numbers include −4, 0, 8, and 1738.
 In particular, zero is an even number.
 Some examples of odd numbers are −5, 3, 9, and 73.
Arithmetic coding is a form of entropy encoding used in lossless data compression.
 Normally, a string of characters such as the words "hello there" is represented using a fixed number of bits per character, as in the ASCII code.
 When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and not-so-frequently occurring characters will be stored with more bits, resulting in fewer bits used in total.
 Arithmetic coding differs from other forms of entropy encoding, such as Huffman coding, in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, an arbitrary-precision fraction "q" where 0.0 ≤ "q" < 1.0.
 It represents the current information as a range, defined by two numbers.
 Recent Asymmetric Numeral Systems family of entropy coders allows for faster implementations thanks to directly operating on a single natural number representing the current information.
Roulette is a casino game named after the French word meaning "little wheel".
 In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even, or if the numbers are high (19–36) or low (1–18).
PartyCasino is an online casino first launched in 1997 under the name Starluck Casino before relaunching again in 2006 as a fully integrated platform.
 The casino offers over 500 games ranging from casino classics like Blackjack and Roulette to a wide variety of online slots.

Question: What game at ParyCasino allows you to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even, or if the numbers are high (19–36) or low (1–18).
Answer: Roulette