Year: 2024
Type: preprint
Abstract: 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 $\mathcal{H}$ 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 $\mathcal{H}$ and characterize all extremal hypergraphs that attain the value, which strengthens and extends the hypergraph version of the classic Erdős-Gallai Theorem.
Source: arXiv (Cornell University)
Authors: Zhao, Kai, Zhang, Xiao-Dong
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393726807