Recognition of chordal graphs and cographs which are Cover-Incomparability graphs
Arun Anil, Manoj Changat

TL;DR
This paper characterizes certain chordal graphs and cographs that are Cover-Incomparability graphs and provides linear-time algorithms for recognizing them.
Contribution
It offers a structural characterization of chordal graphs and cographs that are C-I graphs and develops efficient recognition algorithms.
Findings
Chordal graphs with at most two independent simplicial vertices are C-I graphs.
Similar characterization applies to cographs.
Linear-time recognition algorithms are derived for these classes.
Abstract
Cover-Incomparability graphs (C-I graphs) are an interesting class of graphs from posets. A C-I graph is a graph from a poset with vertex set , and the edge-set is the union of edge sets of the cover graph and the incomparability graph of the poset. The recognition of the C-I graphs is known to be NP-complete (Maxov\'{a} et al., Order 26(3), 229--236(2009)). In this paper, we prove that chordal graphs having at most two independent simplicial vertices are exactly the chordal graphs which are also C-I graphs. A similar result is obtained for cographs as well. Using the structural results of these graphs, we derive linear time recognition algorithms for chordal graphs and cographs which are C-I graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems
