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# Incompressibility of H-free edge modification problems: Towards a dichotomy

Given a graph G and an integer k, the H-free Edge Editing problem is to find whether there exist at most k pairs of vertices in G such that changing the adjacency of the pairs in G results in a graph without any induced copy of H. Nontrivial polynomial kernels are known to exist for some graphs H with at most 4 vertices, but starting from 5 vertices, polynomial kernels are known only if H is either complete or empty. This suggests the conjecture that there is no other H with at least 5 vertices where H-free Edge Editing admits a polynomial kernel. Towards this goal, we obtain a set of nine 5-vertex graphs such that if for every , H-free Edge Editing is incompressible and the complexity assumption holds, then H-free Edge Editing is incompressible for every graph H with at least five vertices that is neither complete nor empty. We obtain similar results also for H-free Edge Deletion/Completion.

## History

## Preferred Citation

Dániel Marx and R.B. Sandeep. Incompressibility of H-free edge modification problems: Towards a dichotomy. In: Journal of Computer and System Sciences. 2022.## Primary Research Area

- Trustworthy Information Processing

## Legacy Posted Date

2022-04-29## Journal

Journal of Computer and System Sciences## Pages

25 - 58## Open Access Type

- Green

## Sub Type

- Article

## BibTeX

@article{cispa_all_3629, title = "Incompressibility of H-free edge modification problems: Towards a dichotomy", author = "Marx, Dániel and Sandeep, R.B.", journal="{Journal of Computer and System Sciences}", year="2022", }## Usage metrics

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