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On the complexity of cover-incomparability graphs of posets. (English) Zbl 1172.05049
The cover-incomparability graph (or C-I graph) $$G$$ of a poset $$P=(V,\leq)$$ has vertex set $$V$$, and two vertices $$x$$ and $$y$$ are adjacent in $$G$$ if $$x$$ covers $$y$$ in $$P$$, or $$y$$ covers $$x$$ in $$P$$, or $$x$$ and $$y$$ are incomparable in $$P$$, see B. Brešar, M. Changat, S. Klavžar, M. Kovše, J. Mathews, and A. Mathews [Order 25, No. 4, 335–347 (2008; Zbl 1219.06004)]. The recognition problem for C-I graphs is NP-complete, but the induced subgraphs of C-I graphs form exactly the class of cocomparability graphs, and can therefore be recognised in linear time, see R. M. McConnell and J. P. Spinrad [Discrete Math. 201, No. 1-3, 189–241 (1999; Zbl 0933.05146)].

##### MSC:
 05C75 Structural characterization of families of graphs 05C62 Graph representations (geometric and intersection representations, etc.) 06A07 Combinatorics of partially ordered sets 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
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##### References:
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