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原文連結
論文資訊
- 類型：已發表論文
- 日期：2020
摘要
We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-case 計算 hardness for this problem in sparse random regular graphs, showing optimality of a simple spectral certificate. This evidence takes the form of a 計算ly-quiet planting: we construct a distribution of d-regular graphs that has significantly smaller chromatic number than a typical regular graph drawn uniformly at random, while providing evidence that these two distributions are indistinguishable by a large class of algorithms. We generalize our results to the more general problem of certifying an upper bound on the maximum k-cut. This quiet planting is achieved by minimizing the effect of the planted structure (
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