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The computational complexity of graph contractions I: Polynomially solvable and NP‐complete cases
Author(s) -
Levin Asaf,
Paulusma Daniel,
Woeginger Gerhard J.
Publication year - 2008
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20214
Subject(s) - combinatorics , mathematics , computational complexity theory , time complexity , discrete mathematics , vertex (graph theory) , line graph , graph , algorithm
For a fixed pattern graph H , let H ‐C ONTRACTIBILITY 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 ‐C ONTRACTIBILITY 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 ‐C ONTRACTIBILITY 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