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Can someone explain to me the definition of a Restricted Hamiltonian Cycle?
I know what a Hamiltonian Path (and a Hamiltonian Cycle) is, but I'm having a problem understanding a what is a Restricted Hamiltonian Cycle exactly.

Thank you.

shapiro yaacov
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XandY
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    Where did you hear this phrase? – shapiro yaacov Dec 07 '15 at 08:33
  • I haven't heared of the notion either. Is this question related to [this](http://link.springer.com/chapter/10.1007/978-1-84800-998-1_7)? – Codor Dec 07 '15 at 08:38
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    I'm voting to close this question as off-topic because it is not programming-related. – n. m. could be an AI Dec 07 '15 at 08:39
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    I would say it could be any restriction that the author of that term came up with. There is not general definition what this restriction would be. See for instance the link by @Codor. – Vincent van der Weele Dec 07 '15 at 08:43
  • I'm preparing for a coming exam, where one of the questions in my algorithm class is to prove that a Restricted Hamiltonian Cycle is NP-Complete. – XandY Dec 07 '15 at 09:03
  • Since a Hamiltonian Cycle is NP-complete, adding any restriction over that wouldn't exactly help make it easier. Unless of course it makes the number of eligible edges 0 or something like that... – shapiro yaacov Dec 07 '15 at 09:08
  • @n.m., I actually did - before I wrote the first comment. If you read the comments above, you can see what has been said up to this point. All I said was that the original question (the original Hamilton Path question) is by itself already NP-complete. – shapiro yaacov Dec 07 '15 at 09:19
  • There is no restricted Hamiltonian cycle. There is a restricted Hamiltonian cycle *problem*. The problem is restricted, not the cycle. – n. m. could be an AI Dec 07 '15 at 09:30
  • @n.m. - on the one hand you are right; It is the name of a *problem*. On the other hand, If I construct a Hamilton cycle made only of edges marked as "blue", what would you call that? – shapiro yaacov Dec 07 '15 at 09:49
  • @shapiroyaacov I would call it a Hamiltonian cycle in the blue subgraph, or something. This is not the point. No one cares what I would call this or that. RHCP is a standard name of a standard problem. Try proving it's NP-hard before inventing an unrelated entity and giving it a confusingly similar name. – n. m. could be an AI Dec 07 '15 at 10:13
  • A proof can be found [here](https://books.google.com/books?id=nkeqCAAAQBAJ&pg=PA185&lpg=PA185&dq="restricted+hamiltonian+cycle+problem"). – n. m. could be an AI Dec 07 '15 at 10:41
  • This type of question will probably get a better answer on http://cs.stackexchange.com because it is not practical and limited enough in scope for StackOverflow. – m69's been on strike for years Dec 07 '15 at 21:21

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