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arXiv · 2512.06383

Finding a Maximum Common (Induced) Subgraph: Structural Parameters Revisited

Tesshu Hanaka·Yuto Okada·Yota Otachi·Lena Volk
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Abstract

We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly restricted structural parameters. Our contribution in this paper is to sharply complement the hardness of the problems by showing fixed-parameter tractable cases: both induced and non-induced problems parameterized by max-leaf number and by neighborhood diversity, and the induced problem parameterized by twin cover number. These results almost completely determine the complexity of the problems with respect to well-studied structural parameters. Also, the result on the twin cover number presents a rather rare example where the induced and non-induced cases have different complexity.

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Tesshu Hanaka, Yuto Okada, Yota Otachi, Lena Volk. 2025-12-06. Finding a Maximum Common (Induced) Subgraph: Structural Parameters Revisited. https://arxiv.org/abs/2512.06383

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