避免长Berge循环II,所有$n$的精确边界

IF 0.4 Q4 MATHEMATICS, APPLIED Journal of Combinatorics Pub Date : 2018-07-16 DOI:10.4310/joc.2021.v12.n2.a4
Z. Furedi, A. Kostochka, Ruth Luo
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引用次数: 13

摘要

设$EG_r(n,k)$表示没有长度为$k$或更长的Berge循环的$n$ -顶点$r$ -均匀超图的最大边数。在本工作的第一部分中,我们找到了$EG_r(n,k)$的精确值,并描述了$k-2$除$n-1$和$k\geq r+3$时的极值超图的结构。本文确定了$EG_r(n,k)$并描述了所有$n$当$k\geq r+4$时的极值超图。
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Avoiding long Berge cycles II, exact bounds for all $n$
Let $EG_r(n,k)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph with no Berge cycles of length $k$ or longer. In the first part of this work, we have found exact values of $EG_r(n,k)$ and described the structure of extremal hypergraphs for the case when $k-2$ divides $n-1$ and $k\geq r+3$. In this paper we determine $EG_r(n,k)$ and describe the extremal hypergraphs for all $n$ when $k\geq r+4$.
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来源期刊
Journal of Combinatorics
Journal of Combinatorics MATHEMATICS, APPLIED-
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发文量
21
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