Abstract
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.
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Brešar, B., Changat, M., Klavžar, S. et al. Cover-Incomparability Graphs of Posets. Order 25, 335–347 (2008). https://doi.org/10.1007/s11083-008-9097-1
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DOI: https://doi.org/10.1007/s11083-008-9097-1