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arXiv · 2002.03189

Maximizing the number of independent sets of fixed size in $K_n$-covered graphs

Anyao Wang·Xinmin Hou·Boyuan Liu·Yue Ma
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Abstract

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.

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Anyao Wang, Xinmin Hou, Boyuan Liu, Yue Ma. 2020-02-23. Maximizing the number of independent sets of fixed size in $K_n$-covered graphs. https://arxiv.org/abs/2002.03189

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