# On Subgraph Complementation to H-free Graphs

@article{Antony2022OnSC, title={On Subgraph Complementation to H-free Graphs}, author={Dhanyamol Antony and Jay Garchar and Sagartanu Pal and R. B. Sandeep and Sagnik Sen and R. Subashini}, journal={Algorithmica}, year={2022}, volume={84}, pages={2842 - 2870} }

For a class G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}$$\end{document} of graphs, the problem Subgraph Complement toG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek…

## One Citation

### Cutting a tree with Subgraph Complementation is hard, except for some small trees

- MathematicsLATIN
- 2022

For a graph property Π , Subgraph Complementation to Π is the problem to ﬁnd whether there is a subset S of vertices of the input graph G such that modifying G by complementing the subgraph induced…

## References

SHOWING 1-10 OF 23 REFERENCES

### Subgraph Complementation

- Materials ScienceAlgorithmica
- 2020

A subgraph complement of the graph G is a graph obtained from G by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph G and…

### Incompressibility of H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H$$\end{document}-Free Edge Modification Problem

- Materials ScienceAlgorithmica
- 2014

Given a fixed graph H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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

- MathematicsESA
- 2020

A set of nine 5-vertex graphs whose incompressibility would give a complete classification of the kernelization complexity of H-free Edge Editing for every graph $H$ with at least 5 vertices that is neither complete nor empty.

### Polynomial Kernels for Paw-free Edge Modification Problems

- Mathematics, Computer ScienceTAMC
- 2020

This work answers both questions affirmatively by presenting, respectively, $O (k)$-vertex and $O(k^4)$ -vertex kernels for them as part of an ongoing program that aims at understanding compressibility of H-free edge modification problems.

### A Polynomial Kernel for Paw-Free Editing

- MathematicsIPEC
- 2020

The question of compressibility for one of the last two unresolved graphs H on $4$ vertices is positively answered and the first polynomial kernel for paw-free editing with $O(k^{6})$vertices is given.

### Which Problems Have Strongly Exponential Complexity

- Mathematics, Computer Science
- 2001

A generalized reduction that is based on an algorithm that represents an arbitrary k-CNF formula as a disjunction of 2?nk-C NF formulas that are sparse, that is, each disjunct has O(n) clauses, and shows that Circuit-SAT is SERF-complete for all NP-search problems.

### Edge-Deletion Problems

- Mathematics, Computer ScienceSIAM J. Comput.
- 1981

This paper shows that the edge-deletion problem is NP-complete for the following properties: (1) without cycles of specified length l, or of any length $ \leqq l$, (2) connected and degree-constrained, (3) outerplanar, (4) transitive digraph, (5) line-invertible, (6) bipartite, (7)transitively orientable.

### Dichotomy Results on the Hardness of H-free Edge Modification Problems

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2017

It is proved that these NP-complete problems cannot be solved in parameterized subexponential time, i.e., in time $2^{o(k)}\cd...

### On Switching to H‐Free Graphs

- MathematicsJ. Graph Theory
- 2014

The problem of deciding if, for a fixed graph H, a given graph is switching equivalent to an H-free graph is studied, showing that for H isomorphic to a claw, the problem is polynomial, and giving infinitely many graphs H such that the problems are NP-complete.