Discrete Mathematics & Theoretical Computer Science, Vol 7 (2005)

Font Size:  Small  Medium  Large

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

Nesrine Abbas, Joseph Culberson, Lorna Stewart


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.

Full Text: GZIP Compressed PostScript PostScript PDF original HTML abstract page