科研之友
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摘要
A well-known theorem of Erdos and Gallai (1959) [1] asserts that a graph with no path of length k contains at most 1/2(k - 1)n edges. Recently Gyori et al. (2016) gave an extension of this result to hypergraphs by determining the maximum number of hyperedges in an r-uniform hypergraph containing no Berge path of length k for all values of r and k except for k = r + 1. We settle the remaining case by proving that an r-uniform hypergraph with more than n edges must contain a Berge path of length r + 1.
- 出版日期2018-3
