Left-right planarity test and Julio Lugo: Difference between pages

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Revision as of 18:46, 12 June 2007

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{{Infobox MLB player|

'''Fraysseix-Rosenstiehl's planarity criterion''' is based on the properties of the [[tree]] defined

bgcolor1=#ba313c|

by a '''Depth-First Search'''. Considering any depth-first search of a [[graph]] ''G'', the [[edge|edges]]

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encountered when discovering a [[vertex]] for the first time define a '''DFS-tree''' ''T'' of ''G''. The remaining edges form the '''cotree'''. Three types of patterns define two relations on the set of the cotree edges, namely the '''T-alike''' and '''T-opposite''' relations:

textcolor1=white|

textcolor2=white|

image=Juliolugo.jpg|

width=300|

name=Julio Lugo|

position=Shortstop|

team=Boston Red Sox|

number=23|

bats=Right|

throws=Right|

debutdate=April 15|

debutyear=2000|

debutteam=Houston Astros|

statyear=June 2, 2007|

stat1label=[[Batting average]]|

stat1value=.272|

stat2label=[[Hit (baseball)|Hits]]|

stat2value=950|

stat3label=[[Run (baseball)|Runs scored]]|

stat3value=530|

stat4label=[[Stolen Base|SB]]|

stat4value=142|

teams=<nowiki></nowiki>

*[[Houston Astros]] ([[2000 in baseball|2000]]&ndash;[[2003 in baseball|2003]])

*[[Tampa Bay Devil Rays]] ([[2004 in baseball|2004]]&ndash;[[2006 in baseball|2006]])

*[[Los Angeles Dodgers]] ([[2006 in baseball|2006]])

*[[Boston Red Sox]] ([[2007 in baseball|2007]] - Present)}}

'''Julio Cesar Lugo''' (born on [[November 16]], [[1975]] in [[Barahona]], [[Dominican Republic]]) is a [[Major League Baseball|major league]] [[shortstop]] for the [[Boston Red Sox]]. He bats and throws [[right-handed]].

Lugo starred at Connors State Community College in Warner, Oklahoma prior to being drafted by the Astros. He attended Fort Hamilton High school in Brooklyn, New York where he batted .350 over all. He also played sandlot ball for the Youth Service League in Brooklyn, New York whose alumni include [[Manny Ramirez]] and [[Shawon Dunston]].

In the following figures, simple circle nodes represent vertices, double circle nodes represent subtrees. Twisted segments represent tree paths and curved arcs represent cotree edges (with label of the edge put near the curved arc). In the first figure, <math>\alpha</math> and <math>\beta</math> are T-alike (it means that their low extremities will be on the same side of the tree in every planar drawing); in the next two figures, they are T-opposite (it means that their low extremities will be on different sides of the tree in every planar drawing).

Julio is the older brother of [[baseball]] [[pitcher]] [[Ruddy Lugo]].

{| cellpadding="20"

|[[Image:leftright1.png|300px]]||[[Image:leftright2.png|300px]]||[[Image:leftright3.png|400px]]

|- align="center"

|<math>\alpha</math> and <math>\beta</math> are T-alike||<math>\alpha</math> and <math>\beta</math> are T-opposite||<math>\alpha</math> and <math>\beta</math> are T-opposite

|}

At the 2006 trade deadline, the Dodgers acquired Lugo from the [[Tampa Bay Devil Rays]] for two minor leaguers, [[Joel Guzmán]] and Sergio Pedroza.

:Let ''G'' be a graph and let ''T'' be a DFS-tree of ''G''. The graph ''G'' is [[Planar graph|planar]] if and only if there exists a partition of the cotree edges of ''G'' into two classes so that any two edges belong to a same class if they are T-alike and any two edges belong to different classes if they are T-opposite.

On December 5, 2006 Lugo signed a 4yr/$36m contract with The Boston Red Sox.

{{Combin-stub}}

On December 13, 2006, a press conference was held at 3:30 at Fenway Park to introduce Lugo as the new Red Sox shortstop. Manager Terry Francona and Assistant General Manager Jed Hoyer were on hand.

== References ==

Lugo made a critical error in the fifth inning of a [[June 7]], [[2007]] game against the [[Oakland Athletics]]. The afternoon contest matched Boston's [[Curt Schilling]] against the Athletics' [[Joe Blanton]]. Schilling threw a complete game one hit shut out, defeating Blanton and the A's 1-0. However, if Lugo made the play in the fifth inning as he should have, Schilling would have faced the minimum and Oakland's [[Shannon Stewart]] would not have had a chance to bat in the ninth. To Schilling and the rest of the team's disappointment, Stewart knocked a seeing eye single past [[Alex Cora]], breaking up the no-hit bid.

* H. de Fraysseix and P. Rosenstiehl, ''A depth-first search characterization of planarity'', Annals of Discrete Mathematics '''13''' (1982), 75–80.

Julio Lugo is absolutely useless.

[[Category:Topological graph theory]]

==Accusations of spousal abuse==

On April 30, 2003, Lugo was arrested and charged with assaulting his wife, Mabely Lugo, outside of Minute Maid Park in Houston before playing the [[Atlanta Braves]]. Mabely was treated and released from a hospital, and filed a restraining order against Julio. Mabely originally contended that Julio punched her in the head and slammed her head into the windshield of their car. Julio contested that he was acting in self-defense by blocking an attack by his wife, who hit herself and stumbled into the car, smashing her head into the windshield. Mabely later changed her story to coordinate with her husband's, and dropped the restraining order, however Julio was still tried in court accused of misdemeanor assault. Julio was eventually found not guilty, and he has remained out of trouble from the public eye since this incident.

Julio Lugo is now living in Dorchester. Julio Lugo stole my rims.

==Career statistics==

{{Baseball stats|name = '''Julio Lugo'''|update = February 24,

2007|g=951|ab=3508|r=539|h=964|2b=179|3b=25|hr=70|rbi=353|sb=148|ba = .275|cite=<ref name="espnstats">{{cite web | title =

Julio Lugo | publisher = ESPN.com | date = 2007-05-10 | url = http://sports.espn.go.com/mlb/players/profile?statsId=6451 |

accessdate = 2007-05-10}}</ref>}}

== References ==

<references/>

[[Category:1975 births|Lugo, Julio]]

[[Category:Living people|Lugo, Julio]]

[[Category:Auburn Astros alumni|Lugo, Julio]]

[[Category:Dominican Republic baseball players|Lugo, Julio]]

[[Category:Major league shortstops|Lugo, Julio]]

[[Category:Houston Astros players|Lugo, Julio]]

[[Category:Tampa Bay Devil Rays players|Lugo, Julio]]

[[Category:Los Angeles Dodgers players|Lugo, Julio]]

[[Category:Boston Red Sox players|Lugo, Julio]]

[[ja:フリオ・ルーゴ]]

{{baseball-shortstop-stub}}