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

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. Hedetniemi, Hedetniemi, Laskar and Mulder introduced its maximum number of colors, $\psq(G)$, as an open direction in their foundational work on quorum colorings. We e...

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