European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-12-15 , DOI: 10.1016/j.ejc.2020.103269 Guorong Gao , An Chang
An -uniform hypergraph is linear if every two edges intersect in at most one vertex. Given a family of -uniform hypergraphs , the linear Turán number ex is the maximum number of edges of a linear -uniform hypergraph on vertices that does not contain any member of as a subhypergraph.
Given a graph and a positive integer , the -expansion of is the -graph obtained from by enlarging each edge of with new vertices disjoint from such that distinct edges of are enlarged by distinct vertices. For , we prove the following extension of Kővári–Sós–Turán’s theorem Specially, for , , we prove that which is an improvement of Gerbner, Methuku and Vizer’s result (Gerbner et al., 2019). Moreover, we also prove some sharp bounds for the linear Turán number of .
中文翻译:
二分法Turán问题的线性超图扩展
一个 如果每两个边缘最多相交一个顶点,则均匀超图是线性的。给定一个家庭-一致超图 ,线性图兰数ex 是线性的最大边数 一致超图 不包含的任何成员的顶点 作为超图。
给定图 和一个正整数 , -扩展 是个 -图形 从...获取 通过扩大每个边缘 与 新顶点不相交 这样 被不同的顶点放大。对于,我们证明了Kővári–Sós–Turán定理的以下扩展 特别是 , ,我们证明 这是Gerbner,Methuku和Vizer结果的改进(Gerbner et al。,2019)。此外,我们还证明了线性图兰数的一些尖锐边界。