## 4 Citations

### Parameterized Algorithms for Steiner Tree and Dominating Set: Bounding the Leafage by the Vertex Leafage

- MathematicsWALCOM
- 2022

. Chordal graphs are intersection graphs of subtrees of a tree, while interval graphs are intersection graphs of subpaths of a path. Undirected path graphs are an intermediate class of graphs, deﬁned…

### MaxCut on Permutation Graphs is NP-complete

- MathematicsArXiv
- 2022

In this paper, we prove that the MaxCut problem is NP-complete on permutation graphs, settling a long-standing open problem that appeared in the 1985 column of the Ongoing Guide to NP-completeness by…

### Maximum cut on interval graphs of interval count five is NP-complete

- MathematicsMFCS
- 2021

This paper presents the first NP-completeness proof for MaxCut when restricted to interval graphs with bounded interval count, namely graphs with interval count 5.

## References

SHOWING 1-10 OF 128 REFERENCES

### Some Simplified NP-Complete Graph Problems

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1976

### Parameterized complexity of finding subgraphs with hereditary properties

- MathematicsTheor. Comput. Sci.
- 2000

### Parameterized Complexity of the Clique Partition Problem

- Mathematics, Computer ScienceCATS
- 2008

This paper shows that this problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is fixed parameter tractable if the authors choose the number of cliques as parameter, and shows that in polynomial time, a kernel bounded by k2 can be obtained.

### Complexity of finding embeddings in a k -tree

- Mathematics, Computer Science
- 1987

This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.

### Subexponential Parameterized Algorithm for Interval Completion

- Mathematics, Computer ScienceSODA
- 2016

The first subexponential parameterized algorithm solving Interval Completion in time kO(√k)nO(1) is given, adding IntervalCompletion to a very small list of parameterized graph modification problems solvable in subexp exponential time.

### Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width

- Mathematics, Computer ScienceTheory of Computing Systems
- 2000

It is proved that this is also the case for graphs of clique-width at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications.

### Parameterized Complexity of Independent Set in H-Free Graphs

- Mathematics, Computer ScienceAlgorithmica
- 2020

This paper investigates the complexity of Maximum Independent Set in the class of H -free graphs, that is, graphs excluding a fixed graph as an induced subgraph and provides a framework for solving several other cases, which is a generalization of the concept of iterative expansion accompanied by the extraction of a particular structure using Ramsey’s theorem.

### Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover

- Computer Science, MathematicsTheory of Computing Systems
- 2007

A new method of solving graph problems related to Vertex Cover by enumerating and expanding appropriate sets of nodes and faster algorithms for solving subclasses of the Steiner tree problem on graphs are investigated.

### Parameterized Complexity of Directed Steiner Tree on Sparse Graphs

- Computer Science, MathematicsSIAM J. Discret. Math.
- 2017

The undirected Steiner Tree problem becomes FPT when restricted to sparse classes of graphs such as planar graph, but the techniques used to show this result break down on directed planar graphs.