Abstract
In this paper we show that the recognition problem for C-I graphs of posets is NP-complete. On the other hand, we prove that induced subgraphs of C-I graphs are exactly complements of comparability graphs, and hence the recognition problem for induced subgraphs of C-I graphs of posets is polynomial.
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Maxová, J., Pavlíková, P. & Turzík, D. On the Complexity of Cover-Incomparability Graphs of Posets. Order 26, 229–236 (2009). https://doi.org/10.1007/s11083-009-9117-9
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DOI: https://doi.org/10.1007/s11083-009-9117-9