Recognizing Maximal Unfrozen Graphs with respect to Independent Sets is CO-NP-complete

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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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2005, 7, pp.141-154
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Nesrine Abbas, Joseph Culberson, Lorna Stewart. Recognizing Maximal Unfrozen Graphs with respect to Independent Sets is CO-NP-complete. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2005, 7, pp.141-154. 〈hal-00959035〉

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