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Author

Rafik Sahbi

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Preprint Sep 2026

Upper $k$-Star-Forming Sets, $k$-Independence, and Upper Domination

For a positive integer $k$, let $\beta_k(G)$ be the maximum cardinality of a vertex set inducing maximum degree less than $k$, and let $SF_k(G)$ be the maximum cardinality of a minimal $k$-star-forming set. The known inequality $\beta_k(G)\le SF_k(G)$ suggests asking when equality holds. We place this question in the f...

Rafik Sahbi · 0 citations
Preprint Sep 2026

Upper $k$-Star-Forming Sets, $k$-Independence, and Upper Domination

For a positive integer $k$, let $\beta_k(G)$ be the maximum cardinality of a vertex set inducing maximum degree less than $k$, and let $SF_k(G)$ be the maximum cardinality of a minimal $k$-star-forming set. The known inequality $\beta_k(G)\le SF_k(G)$ suggests asking when equality holds. We place this question in the f...

Rafik Sahbi · 0 citations
Preprint Sep 2026

Sub-quorum colorings of graphs

A sub-quorum coloring is a partial vertex coloring in which every colored vertex sees at least half of its colored closed neighborhood in its own color. We study the maximum number of colors $\psq(G)$ from structural, algorithmic and extremal viewpoints. Every $2$-independent set yields a sub-quorum coloring, so $\psq(...

Hao Ma, Rafik Sahbi, Wen-Lin Zhang · 0 citations

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