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Maximum $k$-colourable induced subgraphs in $(P_5+rK_1)$-free graphs
Cicely Henderson, Evelyne Smith-Roberge, Sophie Spirkl, Rebecca · 2024-10-11 · via math.CO updates on arXiv.org

We show that for any nonnegative integer $r$, the Weighted Maximum List-$k$-Colourable Induced Subgraph problem can be solved in polynomial time for input graphs that do not contain $(P_5+ rK_1)$ as an induced subgraph, and give an explicit algorithm demonstrating this. This answers a question of Agrawal et al.\ (2024).

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