Recognizing CIS graphs is coNP-complete, proved by a polynomial reduction from 3SAT to the complement of the recognition problem.
Chv´ atal, Two research problems on Grillet graphs, Personal Communication, 1992
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How Difficult Is It to Recognize CIS Graphs?
Recognizing CIS graphs is coNP-complete, proved by a polynomial reduction from 3SAT to the complement of the recognition problem.