## Figures from this paper

## 8 Citations

### Hitting forbidden induced subgraphs on bounded treewidth graphs

- MathematicsMFCS
- 2020

The smallest function $f_H(t)$ such that H-IS-Deletion can be solved in time is determined assuming the Exponential Time Hypothesis (ETH), and it is shown that when $H$ deviates slightly from a clique, the function suffers a sharp jump.

### Tight conditional lower bounds for counting perfect matchings on graphs of bounded treewidth, cliquewidth, and genus

- Computer ScienceSODA
- 2016

It is proved that, assuming the counting version of the Strong Exponential-Time Hypothesis (#SETH), the problem of counting perfect matchings • has no (2 --- e)knO(1) time algorithm for any e > 0 on graphs of treewidth k (but it can be solved in time O(nk+1) if a k-expression is given).

### Double-Exponential and Triple-Exponential Bounds for Choosability Problems Parameterized by Treewidth

- Computer Science, MathematicsICALP
- 2016

A matching lower bound is given giving evidence that double-exponential dependence on treewidth may be necessary for the choosability problem, and evidence that an algorithm with running time 2^(2^(o(w)))*n^(O(1)) would violate the Exponential-Time Hypothesis (ETH).

### Parameterized Graph Modification Algorithms

- Mathematics, Computer Science
- 2015

This thesis shows that editing towards trivially perfect graphs, threshold graphs, and chain graphs are all NP-complete, resolving 15 year old open questions and provides several new results in classical complexity, kernelization complexity, and subexponential parameterized complexity.

### Close relatives (of Feedback Vertex Set), revisited

- MathematicsIPEC
- 2021

A common theme of the first two algorithmic results is to represent connectivity properties of the current graph in a state of a dynamic programming algorithm as an auxiliary forest with O(k) nodes, resulting in a 2O(k log k) bound on the number of states for one node of the tree decomposition or cliquewidth expression.

### Reducing graph transversals via edge contractions

- MathematicsMFCS
- 2020

This work proves co-NP-hardness results under some assumptions on the graphs in ${\cal H}$, which implies that Contraction ($\pi$) is co- NP-hard even for fixed $k=d=1$ when $\pi$ is the size of a minimum feedback vertex set or an odd cycle transversal.

### Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

- MathematicsAlgorithmica
- 2020

It is proved that the problem of finding a largest, in terms of the number of vertices, induced subgraph of a graph G that belongs to $\mathcal{C}$ can be solved in $2^{o(n)$ time.

### Finding List Homomorphisms from Bounded-treewidth Graphs to Reflexive Graphs: a Complete Complexity Characterization

- MathematicsSTACS
- 2018

This work proves for every fixed non-interval graph H that if a tree decomposition of width tw(G) is given in the input, then the problem can be solved in time i^*(H)^{tw(G)} n^{O(1)}.

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