Max Weight Independent Set in sparse graphs with no long claws

Symposium on Theoretical Aspects of Computer Science(2023)

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摘要
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^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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