Localized Version of Hypergraph Erdos-Gallai Theorem
arxiv(2024)
摘要
This paper focuses on extensions of the classic Erdős-Gallai Theorem for
the set of weighted function of each edge in a graph. The weighted function of
an edge e of an n-vertex uniform hypergraph ℋ is defined to a
special function with respect to the number of edges of the longest Berge path
containing e. We prove that the summation of the weighted function of all
edges is at most n for an n-vertex uniform hypergraph ℋ and
characterize all extremal hypergraphs that attain the value, which strengthens
and extends the hypergraph version of the classic Erdős-Gallai Theorem.
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