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k-strong spanning local tournaments in locally semicomplete digraphs

机译：在局部半完全有向图中的k-strong跨越局部锦标赛

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摘要

We point out mistakes in two papers previously published in Discrete Applied Mathematics, dealing with highly strongly connected spanning local tournaments in locally semicomplete digraphs. We conjecture that every (2k - 1)-strong locally semicomplete digraph on at least 2k + 1 vertices contains a k-strong spanning local tournament and prove the conjecture for k = 1, 2. We also prove that every 5-strong locally semicomplete digraph which is not semicomplete contains a 3-strong spanning local tournament. We furthermore show that for semicomplete digraphs, which form a proper subclass of locally semicomplete digraphs, 2k - 1 would be the best possible bound and for locally semicomplete digraphs which are not semicomplete we show that the correct bound is at least 2k - 3.
机译：我们在先前发表于《离散应用数学》的两篇论文中指出了错误，这些论文涉及在局部半完全有向图中的高度紧密联系的跨越局部锦标赛。我们推测至少（2k-1）个强半局部有向图在至少2k + 1个顶点上包含一个k强跨度局部锦标赛，并证明k = 1、2的猜想。没有完全完成的有向图包含3个跨度较大的本地锦标赛。我们进一步表明，对于形成局部半完整有向图的适当子类的半完整有向图，2k-1将是最佳可能的边界，对于非半完整的局部半完整有向图，我们表明正确的边界至少为2k-3

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