Subgraph isomorphism in graph classes

@article{Kijima2012SubgraphII,
  title={Subgraph isomorphism in graph classes},
  author={Shuji Kijima and Yota Otachi and Toshiki Saitoh and Takeaki Uno},
  journal={Discret. Math.},
  year={2012},
  volume={312},
  pages={3164-3173}
}

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References

SHOWING 1-10 OF 32 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.

The subgraph isomorphism problem for outerplanar graphs

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 Complexity of Subgraph Isomorphism for Classes of Partial k-Trees

On the complexity of finding iso- and other morphisms for partial k-trees

On the restriction of some NP-complete graph problems to permutation graphs

Permutation graphs are known as a useful class of perfect graphs for which the NP-complete graph problems GRAPH k-COLORABILITY, PARTITION INTO CLIQUES, CLIQUE and INDEPENDENT SET (VERTEX COVER)

A Linear Time Algorithm for Deciding Interval Graph Isomorphism

It is shown that for a somewhat larger class of graphs, namely the chordal graphs, isomorphism is as hard as for general graphs.

Complement reducible graphs

Finding Hamiltonian Circuits in Interval Graphs

  • J. Keil
  • Mathematics
    Inf. Process. Lett.
  • 1985

Bandwidth of Bipartite Permutation Graphs

Efficient algorithms for computing the bandwidth for three graph classes are presented and the former two improve the previously known upper bounds to optimal, and the last one improves recent result, and they give positive answers to some open problems.