论文标题
最大化$ k_n $覆盖图中固定大小的独立集数量
Maximizing the number of independent sets of fixed size in $K_n$-covered graphs
论文作者
论文摘要
如果每个顶点$ g $包含在$ h $中的$ g $中，则图$ g $是$ h $ - $ h $。在本说明中，我们给出了$ k_n $的最大尺寸$ t \ ge 3 $的独立组数量，该图的大小$ n \ ge n+n+t-1 $并确定其极端图。结果回答了Chakraborit和Loh提出的一个问题。该证明使用超图的边缘开关操作，这仍然是独立集的数量，无偏差。
A graph $G$ is $H$-covered by some given graph $H$ if each vertex in $G$ is contained in a copy of $H$. In this note, we give the maximum number of independent sets of size $t\ge 3$ in $K_n$-covered graphs of size $N\ge n+t-1$ and determine its extremal graph. The result answers a question proposed by Chakraborit and Loh. The proof uses an edge-switching operation of hypergraphs which remains the number of independent sets nondecreasing.
