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Cover-Incomparability Graphs of Posets |
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| Authors: | Boštjan Brešar Manoj Changat Sandi Klavžar Matjaž Kovše Joseph Mathews Antony Mathews |
| Institution: | (1) Department of Mathematics and Computer Science, FNM, University of Maribor, Koroška 160, 2000 Maribor, Slovenia;(2) Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia;(3) Department of Futures Studies, University of Kerala, Trivandrum, 695034, India;(4) Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia;(5) University of Maribor, Maribor, Slovenia;(6) Chingamparampil, Vazhapally, Changanacherry, 686103 Kerala, India |
| 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. |
| Keywords: | Poset Underlying graph Transit function Chordal graph Distance-hereditary graph Claw |
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