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.

Source : oai:HAL:hal-00959035v1

Volume: Vol. 7

Published on: January 1, 2005

Submitted on: March 26, 2015

Keywords: extremal,unfrozen,graph,independent set,co-NP-complete,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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