Permutation graphs and unique games
Monika Rosicka, Simone Severini
TL;DR
This paper explores the graph-theoretic properties of unique games by analyzing permutation-labeled graphs, providing conditions for optimal assignments, and relating special cases to known graph problems like EDGE BIPARTIZATION.
Contribution
It introduces a new graph-theoretic framework for understanding unique games, generalizes permutation graphs, and connects XOR games to Latin square-based edge labelings.
Findings
Classical value of a game characterized via permutation graphs
Necessary and sufficient conditions for optimal assignment
Connections established between XOR games and EDGE BIPARTIZATION
Abstract
We study the value of unique games as a graph-theoretic parameter. This is obtained by labeling edges with permutations. We describe the classical value of a game as well as give a necessary and sufficient condition for the existence of an optimal assignment based on a generalisation of permutation graphs and graph bundles. In considering some special cases, we relate XOR games to EDGE BIPARTIZATION, and define an edge-labeling with permutations from Latin squares.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research