<p>These permutations represent the constraints on the labeling. for each edge, there is some set of labellings for the edge's vertices which is legal. Since we are talking about unique games, these legal labellings are limited in the following way: if (u,v) is an edge, then for any possible labeling of u, there exist a single legal labeling of v. This means that we can represent the legal labellings of any edge's vertices by a permutation $\phi :[k] \to [k]$ where $[k]$ is the set of labels.</p>

CC BY-SA 2.5
2010-08-24T11:29:43.580Z
2010-08-24T11:29:43.580Z
yohay kaplan
<p>What do the <a href="https://secure.wikimedia.org/wikipedia/en/wiki/Unique_games_conjecture#Unique_label_cover" rel="nofollow">edge permuations</a> in the unique games conjecture represent?</p>

<cc.complexity-theory><unique-games-conjecture>
Unique games conjecture - edge permutations
Casebash
# Unique games conjecture - edge permutations

(Asked by: username_0 on 2010-08-24)

What do the [edge permuations](https://secure.wikimedia.org/wikipedia/en/wiki/Unique_games_conjecture#Unique_label_cover) in the unique games conjecture represent?

**Tags:** cc.complexity-theory, unique-games-conjecture

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## 1 answers

### Answer by username_1 on 2010-08-24. Score: 3 | Accepted answer

These permutations represent the constraints on the labeling. for each edge, there is some set of labellings for the edge's vertices which is legal. Since we are talking about unique games, these legal labellings are limited in the following way: if (u,v) is an edge, then for any possible labeling of u, there exist a single legal labeling of v. This means that we can represent the legal labellings of any edge's vertices by a permutation $\phi :[k] \to [k]$ where $[k]$ is the set of labels.


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