论文标题
在取消超图上的光谱Turán类型问题
Spectral Turán Type Problems on Cancellative Hypergraphs
论文作者
论文摘要
令$ g $为取消$ 3 $均匀的超图，其中第三个边缘不包含任何两个边的对称差异。同等地，仅当$ 3 $均匀的超graph $ g $是andcellative，并且仅当$ g $ is $ \ {f_4，f_5 \} $ - free，其中$ f_4 = \ {abc，abc，abd，abd，bcd \} $和$ f_5 = \ f_5 = \ {abc，abc，abd，cde，cde，cde \ \ \} $。极端组合主义者的经典结果表明，平衡的完整三方$ 3 $均匀的超图可实现取消超图的最大尺寸，Bollobás首先证明了这一点，后来由Keevash和Mubayi证明。在本文中，我们考虑了取消超图的极端问题。更确切地说，我们确定取消$ 3 $均匀的超图的最大$ p $ - 光谱半径，并表征了极端超图。作为副产品，我们从光谱观点获得了Bollobás的替代证明。
Let $G$ be a cancellative $3$-uniform hypergraph in which the symmetric difference of any two edges is not contained in a third one. Equivalently, a $3$-uniform hypergraph $G$ is cancellative if and only if $G$ is $\{F_4, F_5\}$-free, where $F_4 = \{abc, abd, bcd\}$ and $F_5 = \{abc, abd, cde\}$. A classical result in extremal combinatorics stated that the maximum size of a cancellative hypergraph is achieved by the balanced complete tripartite $3$-uniform hypergraph, which was firstly proved by Bollobás and later by Keevash and Mubayi. In this paper, we consider spectral extremal problems for cancellative hypergraphs. More precisely, we determine the maximum $p$-spectral radius of cancellative $3$-uniform hypergraphs, and characterize the extremal hypergraph. As a by-product, we give an alternative proof of Bollobás' result from spectral viewpoint.
