Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs

@article{Heggernes2015InducedSI,
  title={Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs},
  author={Pinar Heggernes and Pim van 't Hof and Daniel Meister and Yngve Villanger},
  journal={Theor. Comput. Sci.},
  year={2015},
  volume={562},
  pages={252-269}
}

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References

SHOWING 1-10 OF 21 REFERENCES

Induced Subgraph Isomorphism on Interval and Proper Interval Graphs

It is shown that when G is an interval graph and H is a connected proper interval graph, the problem is solvable in polynomial time and fixed parameter tractable when parametrised by the number of connected components of H.

Subgraph isomorphism in graph classes

Edge contractions in subclasses of chordal graphs

Modular decomposition and transitive orientation

Cleaning Interval Graphs

The NP-hardness of the Induced Subgraph Isomorphism problem is shown, and fixed-parameter tractability of the problem with non-standard parameterization is proved, where the parameter is the difference |V(G)|−|V(H)|.

The clique-separator graph for chordal graphs

  • L. Ibarra
  • Mathematics, Computer Science
    Discret. Appl. Math.
  • 2009

Random Separation: A New Method for Solving Fixed-Cardinality Optimization Problems

A new randomized method, random separation, for solving fixed-cardinality optimization problems on graphs, i.e., problems concerning solutions with exactly a fixed number k of elements that optimize solution values is developed.

Domination on Cocomparability Graphs

The authors determine the algorithmic complexity of domination and variants on cocomparability graphs, a class of perfect graphs containing both the interval and the permutation graphs. Minimum

Simple Linear Time Recognition of Unit Interval Graphs