an:06287233
Zbl 1286.05039
Maxov??, Jana; Turz??k, Daniel
Which distance-hereditary graphs are cover-incomparability graphs?
EN
Discrete Appl. Math. 161, No. 13-14, 2095-2100 (2013).
00331895
2013
j
05C12 05C75 06A06
poset; distance-hereditary graphs; Ptolemaic graphs
Summary: In this paper we deal with cover-incomparability graphs of posets, or briefly C-I graphs. These are graphs derived from posets as the edge-union of their cover graph and their incomparability graph. We answer two recently posed open questions. Which distance-hereditary graphs are C-I graphs? Which Ptolemaic (i.e. chordal distance-hereditary) graphs are C-I graphs? It follows that C-I graphs can be recognized efficiently in the class of all distance-hereditary graph whereas recognizing C-I graphs in general is known to be NP-complete.