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Cover-incomparability graphs of posets. (English) Zbl 1219.06004
Summary: Cover-incomparability graphs (C-I graphs, for short) are introduced, whose edge-set is the union of edge-sets of the incomparability and the cover graph of a poset. Posets whose C-I graphs are chordal (resp. distance-hereditary, Ptolemaic) are characterized in terms of forbidden isometric subposets, and a general approach for studying C-I graphs is proposed. Several open problems are also stated.

06A07 Combinatorics of partially ordered sets
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05C75 Structural characterization of families of graphs
Full Text: DOI
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