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" In graph theory, a graceful labeling of a graph with ""m"" edges is a labeling of its vertices with some subset of the integers between 0 and ""m"" inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between ""1"" and ""m"" inclusive. A graph which admits a graceful labeling is called a graceful graph.
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" The name ""graceful labeling"" is due to Solomon W. Golomb; this class of labelings was originally given the name β-labelings by Alexander Rosa in a 1967 paper on graph labelings.
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" A major unproven conjecture in graph theory is the Graceful Tree conjecture or Ringel–Kotzig conjecture, named after Gerhard Ringel and Anton Kotzig, which hypothesizes that all trees are graceful. The Ringel–Kotzig conjecture is also known as the ""graceful labeling conjecture"". Kotzig once called the effort to prove the conjecture a ""disease"".
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" Another weaker version of graceful labelling is the near graceful labeling, in which the vertices can be labeled using some subset of the integers between ""0"" and ""m+1"" inclusive, such that no two vertices share a label, and each edge is uniquely identified by the absolute difference between its endpoints, such that this magnitude lies between ""1"" and ""m+1"" inclusive.
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" Another conjecture in graph theory is the Rosa's Conjecture, named after Alexander Rosa, which says that all triangular cacti are graceful or nearly-graceful.
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"= = = John Radcliff = = =
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" John Young Radcliff (June 29, 1848 – July 26, 1911) was a professional baseball player who played for the Philadelphia Athletics (), Baltimore Canaries (–), Philadelphia Whites (), and Philadelphia Centennials (). He was primarily a shortstop.
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" Radcliffe debuted with the Philadelphia Athletics of the National Association on May 20, 1871. In 28 games, he hit for a .303 batting average with 0 home runs and 22 runs batted in. He also had 5 stolen bases in his first year. The next year, playing for the Baltimore Canaries, he hit his first career home run and picked up 44 RBIs. He recorded 4 triples as well.
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" In 1873, playing for Baltimore, Radcliffe hit a career high 13 doubles and hit 33 runs batted in, with a .286 batting average. In 1874, playing for the Philadelphia Whites, he hit his second and final career home run, tying for the team lead in homers with George Bechtel.
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" In 1874 Radcliff was expelled from baseball for offering an umpire 175 dollars to help the Chicago White Stockings win a game.
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" Radcliffe played his last season in 1875 with the Philadelphia Centennials, appearing in only 5 games, hitting a mediocre .174 with no home runs and no RBI. His final game was on May 24.
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" Radcliffe died in Ocean City, New Jersey, on July 26, 1911 at the age of 65.
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"= = = Historical geographic information system = = =
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" A historical geographic information system (also written as historical GIS or HGIS) is a geographic information system that may display, store and analyze data of past geographies and track changes in time. It can be regarded as a subfield of historical geography and geographic information science.
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" GIS was originally developed for use in environmental sciences, military and for computer assisted cartography. It is the opinion of some that the tools developed for these uses are ill suited for the features of historical data.
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"= = = Pituophis melanoleucus = = =
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" Pituophis melanoleucus, commonly known as the pine snake, is a species of nonvenomous snake in the family Colubridae. The species is endemic to the southeastern United States. Three subspecies are currently recognized as being valid.
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" Three subspecies of ""Pituophis melanoleucus"" are currently recognized: the nominate subspecies ""P. m. melanoleucus"" (Daudin, 1803), the northern pine snake; ""P. m. lodingi"" (Blanchard, 1924), the black pine snake; and ""P. m. mugitus"" (Barbour, 1921), the Florida pine snake.
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" The subspecific name ""lodingi"" is in honor of Danish-born amateur herpetologist Peder Henry Löding (1869-1942), who lived in Alabama.
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" The species has a variety of common names, including: pine snake, pinesnake, common pine snake, bullsnake, black and white snake, carpet snake, chicken snake, common bullsnake, eastern bullsnake, eastern pine snake, horn(ed) snake, New Jersey pine snake, North American pine snake, northern pine snake, pilot snake, and white gopher snake.
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" Adults of ""P. melanoleucus"" are large, growing to in total length (including tail) and are powerfully built. The head is small and somewhat pointed with an enlarged rostral scale that extends upward between the internasal scales. Usually, four prefrontal scales are seen. At midbody are 27-37 rows of keeled dorsal scales. The anal plate is single. The color pattern consists of a light ground color overlaid with black, brown, or reddish-brown blotches.
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" The species ""P. melanoleucus"" is found in the United States in Alabama, Florida, Georgia, Kentucky, Louisiana, Mississippi, New Jersey, North Carolina, South Carolina, Tennessee, Delaware and Virginia. The nominate subspecies occurs in southern New Jersey, southern North Carolina west through South Carolina to northern Georgia, eastern Tennessee, southeastern Kentucky and south into Alabama. ""P. m. lodingi"" occurs from southwestern Alabama to eastern Louisiana, overlapping with ""P. m. mugitus"" from southern South Carolina to Georgia and southern Florida. A population of the subspecies, originating from released or escaped pets, has established itself in the Netherlands in the coastal dunes and dune forests around Wassenaar.
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" The pine snake inhabits pine flatwoods, sandy pine-oak woodlands, prairies, cultivated field, open brushland, rocky desert and chaparral. It occurs from sea level to an elevation of . The pine snake requires well-drained, sandy soils with little vegetation for use as nesting and hibernation sites.
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" The pine snake preys on rats, mice, moles and other small mammals and eggs. It often enters rodent burrows in search of a meal. In these cases, multiple kills are frequent, with the snake pressing the mice against the walls of the burrow. The snake remains underground in cold weather or during the heat of summer days.
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" When disturbed, it often hisses loudly, sometimes flattening its head, vibrating its tail, and eventually striking at an intruder. To make the rattling sound, the snake forces air out of its lungs, vibrating the epiglottis.
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" After mating has taken place in spring, clutches of three to 24 eggs are laid in June–August. The eggs are deposited in sandy burrows or under large rocks or logs and hatch after 64–79 days of incubation. The eggs are adherent and quite large, up to long by wide. Hatchlings measure .
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" The pine snake is classified as least concern on the IUCN Red List, due to its wide distribution and large number of subpopulations; while the total populations appears to be declining, this is likely happening at a slow rate. However, the species is thought to be impacted by continued habitat degradation and destruction. It is present in a variety of protected areas.
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"= = = John Radcliffe = = =
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" John Radcliffe may refer to:
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"= = = John Shanssey = = =
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" John Shanssey (March 23, 1848 – 1919?) was an American boxer, gambler, saloon owner, and Mayor of Yuma, Arizona. He fought Mike Donovan in a bout refereed by a young 21-year-old Wyatt Earp on July 4, 1868 or 1869 in Cheyenne, Wyoming.
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"= = = Konrad II, Count of Württemberg = = =
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" Konrad II (died 1143) was Count of Württemberg. He reigned from 1110 until 1143. He served as marshal of Swabia and advocate of the town of Ulm, and had large possessions in the valleys of the Neckar and the Rems.
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" Konrad's father is unknown, but he is believed to belong to the family of the counts of Veringen (Veringenstadt). The reason to believe so is due to the similarity of the arms of the Counts of Veringen with that of the Counts of Wirtemberg. Thus it is generally assumed that both noble families are related to each other. Konrad's mother Luitgard of Beutelsbach was a sister of his predecessor Konrad I.
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" After the death of Konrad I, he assumed power as heir of castle Wirtemberg. Konrad II appears on May 12, 1110 together with his wife Hadelwig as donator of properties near Göppingen to the monastery Blaubeuren and on December 28, 1122 as a witness of emperor Heinrich V in Speyer (the first time as count, the latter without title but mentioned amongst counts). He died in 1143.
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"= = = Stone Bridge, Virginia = = =
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