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arXiv · 2309.16995

Max Weight Independent Set in sparse graphs with no long claws

Tara Abrishami·Maria Chudnovsky·Cemil Dibek·Marcin Pilipczuk·Paweł Rzążewski
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Abstract

We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami, Dibek, Chudnovsky, Rzążewski, SODA 2022]. First, we show that with an arguably simpler approach we can obtain a faster algorithm with running time $n^{\mathcal{O}(Δ^2)}$, where $n$ is the number of vertices of the instance and $Δ$ is the maximum degree. Then we combine our technique with known results concerning tree decompositions and provide a polynomial-time algorithm for MWIS in graphs excluding a fixed graph whose every component is a subdivided claw as an induced subgraph, and a fixed biclique as a subgraph.

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Tara Abrishami, Maria Chudnovsky, Cemil Dibek, Marcin Pilipczuk, Paweł Rzążewski. 2024-01-12. Max Weight Independent Set in sparse graphs with no long claws. https://arxiv.org/abs/2309.16995

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