Discrete Mathematics & Theoretical Computer Science


Volume 7 n° 1 (2005), pp. 141-154

author:Abbas, N., Culberson, J., and Stewart, L.
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.

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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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