We exhibit an unambiguous k-DNF formula that requires CNF width Omega~(k^{1.5}). Our construction is inspired by the board game Hex and it is vastly simpler than previous ones, which achieved at best an exponent of 1.22. Our result is known to imply several other improved separations in query and communication complexity (e.g., clique vs. independent set problem) and graph theory (Alon--Saks--Seymour problem).

中文翻译：

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十六进制的明确DNF

我们展示了一个明确的k-DNF公式，该公式需要CNF宽度Omega〜（k ^ {1.5}）。我们的构造受到棋盘游戏Hex的启发，并且比以前的游戏要简单得多，后者的最高指数为1.22。众所周知，我们的结果暗示了查询和通信复杂性（例如集团与独立集合问题）和图论（Alon-Saks-Seymour问题）之间的其他几种改进的分离。