The computational complexity of graph contractions II: two tough polynomially solvable cases

Levin, A.; Paulusma, D.; Woeginger, G.J.

Abstract

For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This article is part II of our study on the computational complexity of the H-CONTRACTIBILITY problem. In the first article we pinpointed the complexity for all pattern graphs with five vertices except for two pattern graphs H. Here, we present polynomial time algorithms for these two remaining pattern graphs. 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.

Citation

Levin, A., Paulusma, D., & Woeginger, G. (2008). The computational complexity of graph contractions II: two tough polynomially solvable cases. Networks, 52(1), 32-56. https://doi.org/10.1002/net.20249

• Journal Article Type: Article
• Publication Date: Aug 1, 2008
• Deposit Date: Oct 6, 2010
• Journal: Networks
• Print ISSN: 0028-3045
• Electronic ISSN: 1097-0037
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 1
• Pages: 32-56
• DOI: https://doi.org/10.1002/net.20249
• Keywords: Graph, Edge contraction, Dominating vertex, Wheel, Computational complexity.
• Public URL: https://durham-repository.worktribe.com/output/1538900