论文标题
Fano飞机的RainbowErdős-Rothschild问题
The rainbow Erdős-Rothschild problem for the Fano plane
论文作者
论文摘要
FANO平面是七个顶点和七个超中期的独特线性3-均匀的超图。最近证明，对于所有$ n \ geq 8 $，平衡的完整的两分3-均匀的$ n $顶点上的均匀的超图（由$ b_n $表示）是$ n $ n $ dertices上的3-均匀的超盖，其中最大数量的Hyperedges不包含Fano Plane副本。对于足够大的$ r $和$ n $，我们表明$ b_n $承认$ r $ $ - 边缘的着色数量最多，没有fano飞机的彩虹副本。
The Fano plane is the unique linear 3-uniform hypergraph on seven vertices and seven hyperedges. It was recently proved that, for all $n \geq 8$, the balanced complete bipartite 3-uniform hypergraph on $n$ vertices, denoted by $B_n$, is the 3-uniform hypergraph on $n$ vertices with the largest number of hyperedges that does not contain a copy of the Fano plane. For sufficiently large $r$ and $n$, we show that $B_n$ admits the largest number of $r$-edge colorings with no rainbow copy of the Fano plane.
