Variants of cop and robber problem

Example[ edit ] On a treethe cop number is one. The cop can start anywhere, and at each step move to the unique neighbor that is closer to the robber.

Variants of cop and robber problem

Lieutenant Dangle[ edit ] Lieutenant James "Jim" Ronald Dangle played by Thomas Lennon is the highest-ranking deputy in the department and is usually seen wearing his trademark short-shorts, which he claims that he wears for "mobility.

Unfortunately, his jeans caught fire, forcing Dangle to cut the bottom parts of his pants off, resulting in the hot-pants he currently wears. I guess people think he's closeted because Trudy is in love with him, but that has more to do with the fact that she's severely brain-damaged.

In one episode, Jones apparently had sex with him out of sympathy "I'll try anything once"after which Dangle was hospitalized because, as Jones said it, "he can't fucking walk. Dangle was briefly married to a woman named Debbie see below and he briefly believed that he fathered a son a result of sex with what he thought was a drag queenbut DNA results proved otherwise.

Dangle also felt attracted to a female officer from the Department of Homeland Security who was in Reno to conduct counter-terrorism training but the experience left him uncomfortable and confused. It was revealed later that the female officer was actually a very well-disguised man and was part of a team of con artists, along with the other Homeland Security "trainer"which caused sexual confusion among the heterosexual deputies who had also felt attracted to "her".

Prior to Trudy's brain damage, Dangle apparently had an affair with her while married to Deb in Despite her brain damage, he still engages Trudy romantically on occasion, most notably in Reno !: Miamiwhere Trudy asks Dangle to have sex with her out of pity; to which he tries but fails.

Dangle leads the briefings in the mornings, but often ditches work along with a few other officers, as one time Dangle spent an afternoon trying to destroy an old microwave instead of helping investigate a murder.

He apparently keeps tabs on officers after or during work, as he is found by Johnson in her favorite salon, using her name for an appointment. Dangle is favorable to Jones, and compares Jones to "Glue" saying he and the department are "A little birdhouse that Jones is keeping together.

Dangle engages in police brutality with his fellow officers, as he once beat a suspect to the point of tears after the suspect had insulted him. Dangle looks up to the FBI, as in an episode where a group of FBI agents come to investigate a murder, he makes his officers line up in a perfect order to greet them, and takes on an "Important" mission to get coffee for the agents happily, but resents them for taking his case.

Dangle is a former maitre d' and member of the United States Coast Guard who was stationed in Hawaii and who was discharged from the Coast Guard for reasons undisclosed. In Episodehis age is noted as Dangle was born and raised in Arkansas. Dangle's father abandoned his family when he was a child and his mother committed suicideafter which he was raised by his Uncle Frederick who was kicked out of the Jesuits.

Meanwhile, Dangle's father moved to Chicago and started a new family. Dangle's father had two more African-American children who appear in Episode to visit Dangle after the death of their father to settle the will. Dangle is also the subject of a running gag in which his police bicycle is repeatedly stolen or vandalized.

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It is hinted that Deputy Junior is responsible for these incidents. Dangle carries a Desert Eagle Handgun while hunting for his bike. Deputy Wiegel[ edit ] Deputy Trudy Wiegel played by Kerri Kenney-Silver is a brain-damaged, emotionally unstable, heavily-medicated woman. She is a hypochondriac with multiple psychological disordersoccasional night terrorsand suicidal ideations.

She is a generally neurotic person with low self-esteem and an intense love for cats. She claims to be of Irish and Native American descent. Wiegel enjoys crafts and collecting baby clothes, and is infatuated with Lt. Her favorite picnic location is her mother's grave.

After his arrest and conviction, she continued their relationship via prison visits, both through a glass partition and conjugal visits ; they married on the day of his execution.

Wiegel's father, mentioned in Season 1 and appearing in Season 5, is a Native American. Comedy Central censors removed a second story about her father being lynched by a white mob reacting to news that a non-white man "raped" her mother.

The fourth season began with Wiegel returning after six months of personal leave while pregnant; actress Kerri Kenney-Silver's pregnancy was written into the show.

Wiegel revealed that late husband Craig Pullin wasn't the father he was " shooting blanks " ; she had been artificially inseminated at a local sperm bank.\Cops and Robbers" is an example of a class of games called \pursuit and evasion." The study of pursuit and evasion type games has its roots in the mathematical study of military strategy dating back to destroyer vs.

submarine problems during World. We determine the cop number of the hypercube for different versions of the game Cops and Robber. Cops and Robber is a two player game played on an undirected graph. One player controls some number.

There are many variants. For example, there can be more than one cops and/or robbers. Also, in the above description it is assumed that the cops can see the robber and vice versa. In another version the robber is invisible. There are versions where the robber is faster than the cops (even infinitely faster).

If this never happens, the robber wins. The cop number of a graph is the minimum number such that cops can win the game on. Example. On a tree, the cop number is one. The cop can start anywhere, and at each step move to the unique neighbor that is closer to the robber.

Combinatorics - Another variant of cops and robber. - Mathematics Stack Exchange

Unsolved problem in mathematics: What is the largest possible cop. Ryo Saeba is a "sweeper" (combination hitman/private eye) who uses his Improbable Aiming Skills and all-round badassery to deal with crime in Tokyo. He also happens to be a loony Chivalrous Pervert.. The City Hunter manga by Tsukasa Hojo ran in Weekly Shounen Jump from to It spawned four anime series, several OVAs and a live-action movie starring Jackie Chan.

Cops-and-robbers: remarks and problems Michel Boyera,1, Sif El Harti a, Amal El Ouarari, Robert Ganianb, let us x a graph G. The players are the cop and the robber (for future reference we can think of them as tokens to be placed on It is a long-standing open problem to characterize k cop-win graphs for.).

Variants of cop and robber problem
Cop number - Wikipedia