| 研究実績の概要 |
As a result of this project, we have obtained a wide variety of algorithmic, complexity theoretic and graph theoretic results, in particular from the point of view of parameterized complexity and width parameters. Some highlights of the results obtained during the project include solving the computation complexity of the Independent Set Reconfiguration problem for the token sliding rule on split graph, which was a long-standing open problem, and identifying the first problem that distinguishes treewidth from path-width from the point of view of parameterized tractability, namely Grundy coloring. Together, the results we obtained help refine understanding of the complexity landscape of various fundamental graph-theoretic computational problems, especially from the point of view of width-parameters. We also obtained other various results, such as an in-depth study of the classical and parameterized complexity of finding large odd subgraphs and odd colorings of graphs. In particular, we studied the parameterized complexity of such problems under the graphs parameter rank-width, and proved that those problems can be solved in single-exponential time when parameterized by rank-width, the first problems shown to have this property. This distinguise those problems from their classical, non-parity variants, which, as far as current knowledge goes, require super-exponential running-time to be solved. We hope these results will pave the way to a better understanding of the differences between rank-width and clique-width (a parameter closely related to rank-width).
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