Recognition of chordal graphs and cographs which are Cover-Incomparability graphs
Résumé
Cover-Incomparability graphs (C-I graphs) are an interesting class of graphs from posets. A C-I graph is a graph from a poset P = (V, ≤) with vertex set V , 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 (Maxová 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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Recognition_Algorithm_chordal_cograph.pdf (524.11 Ko)
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chordal_cograph.eps (134.4 Ko)
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claw.eps (164.69 Ko)
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clique-tree.eps (295.43 Ko)
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cograph.eps (627.7 Ko)
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cograph_cotree.eps (533.08 Ko)
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cotree_example.eps (223.48 Ko)
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