On Contracting Graphs to Fixed Pattern Graphs
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Contractions of planar graphs in polynomial time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Contracting planar graphs to contractions of triangulations
Journal of Discrete Algorithms
Edge contractions in subclasses of chordal graphs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Contracting a chordal graph to a split graph or a tree
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Containment relations in split graphs
Discrete Applied Mathematics
On graph contractions and induced minors
Discrete Applied Mathematics
Edge contractions in subclasses of chordal graphs
Discrete Applied Mathematics
Finding contractions and induced minors in chordal graphs via disjoint paths
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Increasing the minimum degree of a graph by contractions
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Detecting induced star-like minors in polynomial time
Journal of Discrete Algorithms
Contracting chordal graphs and bipartite graphs to paths and trees
Discrete Applied Mathematics
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For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This paper is part I of our study on the computational complexity of the H-CONTRACTIBILITY problem. We continue a line of research that was started in 1987 by Brouwer and Veldman, and we determine the computational complexity of the H-CONTRACTIBILITY problem for certain classes of pattern graphs. In particular, we pinpoint the complexity for all graphs H with five vertices except for two graphs, whose polynomial time algorithms are presented in part II. Interestingly, in all connected cases that are known to be polynomially solvable, the pattern graph H has a dominating vertex, whereas in all cases that are known to be NP-complete, the pattern graph H does not have a dominating vertex. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008 An earlier version of this paper appeared in the Proceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2003).