Abstract
For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. We continue a line of research that was started in 1987 by Brouwer & Veldman, and we determine the computational complexity of H-CONTRACTIBILITY for certain classes of pattern graphs. In particular, we pin-point the complexity for all graphs H with five vertices.
Interestingly, in all 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.
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References
Brouwer, A.E., Veldman, H.J.: Contractibility and NP-completeness. Journal of Graph Theory 11, 71–79 (1987)
Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Co., New York (1979)
Robertson, N., Seymour, P.D.: Graph minors. XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B 63, 65–110 (1995)
Watanabe, T., Ae, T., Nakamura, A.: On the NP-hardness of edge deletion and edge-contraction problems. Discrete Applied Mathematics 6, 63–78 (1981)
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© 2003 Springer-Verlag Berlin Heidelberg
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Levin, A., Paulusma, D., Woeginger, G.J. (2003). The Complexity of Graph Contractions. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_28
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DOI: https://doi.org/10.1007/978-3-540-39890-5_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20452-7
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