The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Contractions of planar graphs in polynomial time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On graph contractions and induced minors
Discrete Applied Mathematics
Edge contractions in subclasses of chordal graphs
Discrete Applied Mathematics
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We study the following two graph modification problems: given a graph G and an integer k, decide whether G can be transformed into a tree or into a path, respectively, using at most k edge contractions. These problems, which we call Tree Contraction and Path Contraction, respectively, are known to be NP-complete in general. We show that on chordal graphs these problems can be solved in O(n+m) and O(nm) time, respectively. As a contrast, both problems remain NP-complete when restricted to bipartite input graphs.