Finding a Maximum Common (Induced) Subgraph: Structural Parameters Revisited
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.
Cite
@article{arxiv.2512.06383,
title = {Finding a Maximum Common (Induced) Subgraph: Structural Parameters Revisited},
author = {Tesshu Hanaka and Yuto Okada and Yota Otachi and Lena Volk},
journal= {arXiv preprint arXiv:2512.06383},
year = {2025}
}
Comments
16 pages, 1 figure, WALCOM 2026