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As a continuation of the study of cover-incomparability graphs of posets (C-I graphs), the notion of 2-colored diagrams is introduced and used in characterizations of posets whose C-I graphs belong to certain natural classes of graphs. As a particular instance, posets whose C-I graphs are chordal are characterized using a single 2-colored diagram. Some other instances are characterized in a similar way.

The cover-incomparability graph of a poset P is the edge-union of the covering and the incomparability graph of P. As a continuation of the study 3-colored diagrams we characterize some forbidden ⊲ -preserving subposets of the posets whose cover-in comparability graphs are not line graphs is proved.

The notion of forbidden ⊲-preserving 2-colored and 3-colored diagrams is introduced here as part of the study of cover-incomparability graphs of posets. Posets whose C-I graphs are chordal, which are characterized here using 2-colored and 3-colored diagrams.