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In a lecture I'm taking about complexity theory a professor said, there are infinite many NP-complete problems.

Question:

I was wondering if there exists something like a database or a book with some known reductions (or with maybe more than only the NP-complete ones) and the proofs for them? I know there is a very nice database for Rings, but I couldn't find something similar for reductions.

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    $\begingroup$ As a side note: There is an infinite number of $NP$-complete problems. Simply take your favorite $NP$-complete problem, and call it $L$. For any $k\ge 0$ we have that $0^kL$ is also $NP$-complete. Since we can choose an infinite number of $k$'s, we also must have an infinite number of $NP$-complete problems. $\endgroup$
    – nir shahar
    Oct 5 at 22:25
  • $\begingroup$ Ahm yes...I've edited my question :) $\endgroup$
    – Algebruh
    Oct 5 at 22:27
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    $\begingroup$ Though not containing the actual reductions, the standard reference is Garey & Johnson. $\endgroup$ Oct 6 at 7:00
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    $\begingroup$ An interactive database of reductions similar to ISGCI would be pretty neat. If it doesn't exist, it might be a fun student project to make one. $\endgroup$
    – Discrete lizard
    Oct 6 at 7:20
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The classical reference on NP-completeness is Garey and Johnson's Computers and Intractability, which contains a compendium of over 300 NP-complete problems, with links to papers proving their NP-hardness. The only downside is that the book is quite old, dating from 1979.

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