# Discrete Mathematics & Theoretical Computer Science

## Volume 7 n° 1 (2005), pp. 141-154

author: | Abbas, N., Culberson, J., and Stewart, L. |
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title: | Recognizing Maximal Unfrozen Graphs with respect to Independent Sets is CO-NP-complete |

keywords: | graph, independent set, co-NP-complete, extremal, unfrozen |

abstract: | A graph is unfrozen with respect to k independent set if it has an independent set of size k after the addition of any edge. The problem of recognizing such graphs is known to be NP-complete. A graph is maximal if the addition of one edge means it is no longer unfrozen. We designate the problem of recognizing maximal unfrozen graphs as MAX(U(k-SET)) and show that this problem is CO-NP-complete. This partially fills a gap in known complexity cases of maximal NP-complete problems, and raises some interesting open conjectures discussed in the conclusion. If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Abbas, N., Culberson, J., and Stewart, L. (2005),
Recognizing Maximal Unfrozen Graphs with respect to Independent Sets is CO-NP-complete,
Discrete Mathematics and Theoretical Computer Science 7, pp. 141-154 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Tue Aug 30 22:04:12 CEST 2005 by falk