Edge contractions in subclasses of chordal graphs

@inproceedings{Belmonte2011EdgeCI,
  title={Edge contractions in subclasses of chordal graphs},
  author={R{\'e}my Belmonte and Pinar Heggernes and Pim van 't Hof},
  booktitle={Discrete Applied Mathematics},
  year={2011}
}
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The Contractibility problem takes as input two graphs G and H, and the task is to decide whether H can be obtained from G by a sequence of edge contractions, which is known to be NP-complete when k=2, and can be solved in polynomial time on chordal graphs even when k is part of the input.

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Polynomial-time algorithms for Subgraph Isomorphism in small graph classes of perfect graphs

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A note on contracting claw-free graphs

This work considers the problems that are to test whether a given host graph contains a fixed target graph as a contraction, and shows that these problems may become computationally easier when the host graphs are restricted to be claw-free.

Increasing the minimum degree of a graph by contractions

Contracting a Chordal Graph to a Split Graph or a Tree

It is shown that containment relations extending SUBGRAPH ISOMORPHISM can be solved in linear time if G is a chordal input graph and H is an arbitrary graph not part of the input.

Induced Subtrees in Interval Graphs

It is shown that the closely related Subtree Isomorphism problem is NP-complete even when G is restricted to the class of proper interval graphs, a well-known subclass of interval graphs.

Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs

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