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Structure of tight (k,0)-stable graphs

Dingding DongSammy Luo
Jan 2024
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摘要原文
We say that a graph G is $(k,\ell)$-stable if removing $k$ vertices from it reduces its independence number by at most $\ell$. We say that G is tight $(k,\ell)$-stable if it is $(k,\ell)$-stable and its independence number equals $\lfloor{\frac{n-k+1}{2}\rfloor}+\ell$, the maximum possible, where $n$ is the vertex number of G. Answering and question of Dong and Wu, we show that every tight $(2,0)$-stable graph with odd vertex number must be an odd cycle. Moreover, we show that for all $k\geq 3$, every tight $(k,0)$-stable graph has at most $k+6$ vertices.
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