An earlier version of this paper appeared in the Proceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2003).
The computational complexity of graph contractions I: Polynomially solvable and NP-complete cases†
Article first published online: 14 DEC 2007
Copyright © 2007 Wiley Periodicals, Inc.
Volume 51, Issue 3, pages 178–189, May 2008
How to Cite
Levin, A., Paulusma, D. and Woeginger, G. J. (2008), The computational complexity of graph contractions I: Polynomially solvable and NP-complete cases. Networks, 51: 178–189. doi: 10.1002/net.20214
- Issue published online: 8 APR 2008
- Article first published online: 14 DEC 2007
- Manuscript Accepted: MAY 2007
- Manuscript Received: MAR 2006
- edge contraction;
- dominating vertex;
- computational complexity
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