Samenvatting
We consider the Π-FREE DELETION problem parameterized by the size of a vertex cover, for a range of graph properties Π. Given an input graph G, this problem asks whether there is a subset of at most k vertices whose removal ensures the resulting graph does not contain a graph from Π as an induced subgraph. We introduce the concept of characterizing a graph property Π by low-rank adjacencies, and use it as the cornerstone of a general kernelization theorem for Π-FREE DELETION parameterized by the size of a vertex cover. The resulting framework captures problems such as AT-FREE DELETION, WHEEL-FREE DELETION, and INTERVAL DELETION. Moreover, our new framework shows that the vertex-deletion problem to perfect graphs has a polynomial kernel when parameterized by vertex cover, thereby resolving an open question by Fomin et al. (2014) [18].
Originele taal-2 | Engels |
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Pagina's (van-tot) | 59-79 |
Aantal pagina's | 21 |
Tijdschrift | Journal of Computer and System Sciences |
Volume | 126 |
DOI's | |
Status | Gepubliceerd - jun. 2022 |
Bibliografische nota
Publisher Copyright:© 2021 The Author(s)
Financiering
Funding: This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 803421 , ReduceSearch). Image 1 Image 2