Leírás
A Berge path of length $k$ in an $r$-uniform hypergraph is a collection
of $k$ hyperedges $h_1,\dots,h_k$ and $k+1$ vertices $v_1,\dots,v_{k+1}$
such that $v_i, v_{i+1}\in h_i$ for each $1\le i\le k$. Gy\H{o}ri,
Katona and Lemons [\textit{European J. Combin. 58 (2016) 238--246}]
generalized the Erd\H{o}s-Gallai theorem to Berge paths and established
bounds for the Tur\'{a}n number of Berge paths. However, these bounds
are sharp only when some divisibility conditions hold. Gy\H{o}ri,
Lemons, Salia and Zamora [\textit{J. Combin. Theory Ser. B 148 (2021)
239--250}] determined the exact value of the Tur\'{a}n number of Berge
paths in the case $k\leq r$. In this paper, we settle the final open
case $k>r$, thereby completing the determination of the Tur\'{a}n number
of Berge paths.
This is a joint work with Xin Cheng, Dániel Gerbner, Shujing Miao and
Junpeng Zhou.
Meeting ID
895 2960 8626
Passcode627606
Invite Link https://us06web.zoom.us/j/89529608626?pwd=Y4YMgg9b3QvdPmbym7JPMTvyNMpPwb.1