Which distance-hereditary graphs are cover-incomparability graphs?

Authors:
Jana Maxová;Daniel TurzíK
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 3
Cited 1

Distance-hereditary graphs

Journal of Combinatorial Theory Series B
Graph classes: a survey

Graph classes: a survey
Cover-incomparability graphs and chordal graphs

Discrete Applied Mathematics

Which k-trees are cover-incomparability graphs?

Discrete Applied Mathematics

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Abstract

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.