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arXiv · 2606.22972

On externally supported independence number of graphs

Dragana Božović·Iztok Peterin·Adriana Roux·Aleksandra Tepeh
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Abstract

We introduce the \emph{externally supported independence number} $\alpha_{\rm es}(G)$ of a graph $G$ as the maximum cardinality of an independent set $B$ with an additional condition, that vertices from $N(B)$ are dominated by vertices in $V(G)-N[B]$. This parameter yields an improved upper bound on the isolation number $\iota(G)$. We show that computing $\alpha_{\rm es}(G)$ is NP-hard, while for trees we present a linear-time algorithm. We also establish several sharp bounds on $\alpha_{\rm es}(G)$ for general graphs, with additional refined results for trees. In several cases, we completely describe the extreme graph classes attaining these bounds.

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Dragana Božović, Iztok Peterin, Adriana Roux, Aleksandra Tepeh. 2026-06-22. On externally supported independence number of graphs. https://arxiv.org/abs/2606.22972

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