论文标题
凸几何超图中的紧密路径
Tight paths in convex geometric hypergraphs
论文作者
论文摘要
在本文中，我们证明了在凸几何超图中的紧密路径上的定理，在无限的许多情况下，该定理在渐近上是渐近的。我们的几何定理是Hopf和Pannwitz [12]，Sutherland [19]，Kupitz和Perles [16]的常见概括，用于凸几何图，以及经典的ERDőS-GALLAI定理[6]。结果，我们在统一超图中的紧密路径上获得了Turán问题的第一个实质性改善。
In this paper, we prove a theorem on tight paths in convex geometric hypergraphs, which is asymptotically sharp in infinitely many cases. Our geometric theorem is a common generalization of early results of Hopf and Pannwitz [12], Sutherland [19], Kupitz and Perles [16] for convex geometric graphs, as well as the classical Erdős-Gallai Theorem [6] for graphs. As a consequence, we obtain the first substantial improvement on the Turán problem for tight paths in uniform hypergraphs.
