超图中超星不交并的Turán数  

The Turán Number of Disjoint Stars in Hypergraphs

作　　者：邓静华 侯建锋 曾庆厚 张一枭 Deng Jinghua;Hou Jianfeng;Zeng Qinghou;Zhang Yixiao(Center for Discrete Mathematics and Theoretical Computer Science,Fuzhou University,Fuzhou 350003,China)

机构地区：[1]福州大学离散数学与理论计算机科学研究中心,福州350003

出　　处：《数学理论与应用》2023年第1期64-73,共10页Mathematical Theory and Applications

基　　金：National Natural Science Foundation of China(Nos.12071077,12001106);National Natural Science Foundation of Fujian Province(No.2021J05128)。

摘　　要：给定一个r一致超图F,F的Turán数exr(n,F)表示n个顶点不含F作为子图的r一致超图的最大边数.当r≥3时,确定exr(n,F)是一件非常困难的事情,尤其是当exr(n,F)=o(n^(r))时.对于一个图F,F的扩张F^(+)是指在图F的每条边上添加r−2个新的点所得到的r一致超图;F的Berge超图BergeF是一个r一致超图H,满足V(F)⊆V(H)并且存在一个从E(F)到E(H)的双射f,使得对于每个e∈E(F),e⊆f(e).在本文中,我们确定超图中超星不交并的扩张及其Berge超图的Turán数,这是Khormali和Palmer[14]的结果的推广.Given an runiform hypergraph F,the Turán number of F,denoted by exr(n,F),is the maximum number of edges in an Ffree runiform hypergraph on n vertices.For r≥3,determining exr(n,F)is known to be notoriously hard especially when exr(n,F)=o(n^(r)).For a graph F,the expansion of F,denoted by F^(+),is an runiform hypergraph by adding r−2 new elements to each edge of F;and the Berge copy of F,denoted by BergeF,is an runiform hypergraph H with V(F)⊆V(H)satisfying that there is a bijection f from E(F)to E(H)such that e⊆f(e)for every e∈E(F).In this paper,we determine the Turán numbers of the expansion,and the family of all Berge copy of disjoint union of stars.Both generalize the results given by Khormali and Palmer[14].

关 键 词：Turán数 星 扩张 Berge超图 

分 类 号：O157.5[理学—数学]