Talk:Unique games conjecture

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Failed to Parse

When I load this page, there's a big red "Failed to Parse" on it at the bottom of the "Unique Label Cover" section. Can someone (who knows more about the UGC) take a look at that? — Preceding unsigned comment added by 142.244.222.54 (talk) 18:40, 9 February 2014 (UTC)[reply]

Missing

This page is missing any substantial discussion of why the UGC is important. Also missing are equivalent forms of the conjecture, e.g., 2LIN(q). 131.215.48.236 (talk) 22:29, 29 May 2008 (UTC)[reply]

Clarify for non-experts

I've added another reference that is good for non-experts, and made another one more prominent. We should mine them for insights to improve this important article, helping make it more accessible.★NealMcB★ (talk) 01:08, 30 October 2012 (UTC)[reply]

The UGC bound for Max-2-SAT

In this reference, the bound β achieved on Max-2-SAT in Theorem 3 is .943943... which is larger than .940... Is this an error, or does another paper prove the tight bound? --125.34.6.194 (talk) 02:38, 27 October 2013 (UTC)[reply]

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Unique label cover

For each edge, the colors on the two vertices are restricted to some particular ordered pairs Do you mean to say that there are k ordered pairs and each color appears at each vertex exactly once? (otherwise I don't see how you would get uniqueness) This means that an instance of label cover with unique constraints over an alphabet of size k can be represented as a directed graph together with a collection of permutations πe: [k] → [k], one for each edge e of the graph Such instances are strongly constrained in the sense that the colour of a vertex uniquely defines the colours of its neighbours

That is what it usually means, yes. It isn't a very interesting problem if you're asking for all the constraints to be satisfied (just pick a color for one vertex and propagate) but the problem is, for cases that can't all be satisfied, to satisfy approximately as many constraints as possible. —David Eppstein (talk) 20:52, 26 October 2018 (UTC)[reply]

which English to use

because there are uses of the different colour/color Awesomecat713 (talk) 16:28, 25 June 2021 (UTC)[reply]

Khot 2002 uses "color" so I think as the foundational document for this topic that is what we should follow. Our article was created in 2005 but the "colour" spelling appears to have been added in 2010, much later. —David Eppstein (talk) 16:50, 25 June 2021 (UTC)[reply]