On the Complexity of Cover-Incomparability Graphs of Posets

Maxová, Jana; Pavlíková, Pavla; Turzík, Daniel

doi:10.1007/s11083-009-9117-9

Cited by 11 publications

(6 citation statements)

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“…The studies on C-I graphs is interesting due to the fact that C-I graphs belong to some interesting classes of graphs like hole-free graphs [8] and perfect graphs [1], but a nice graph-theoretic characterization of C-I graphs is still unknown. It is proved that the recognition complexity of C-I graphs is NP-complete (Maxová et al in [11]). Several authors considered the problem of characterizing C-I graphs from well-known graph families: split graphs, block graphs [6], cographs [7], Ptolemaic graphs [12], distance-hereditary graphs [12], and k-trees [10].…”

Section: Introductionmentioning

confidence: 99%

Composition and product of cover-incomparability graphs

Changat

Anil

2022

Art Discrete Appl. Math.

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Cover-Incomparability graphs (C-I graphs) form an interesting class of graphs arising from posets. A few classes of graphs are known to be C-I graphs so far. Composition operation and various graph products are usually used to produce more non-trivial graphs in a particular graph class, using the prime graphs in the class. In this paper, we attempt to study the effect of the composition, lexicographic and strong products of C-I graphs. We found that the lexicographic product of two C-I graphs, say G and H is a C-I graph if and only if either G is any C-I graph, and H is a complete graph or vice versa. A similar result holds for the strong product also. It can be observed that the composition operation is more general than lexicographic product and we obtain new classes of C-I graphs from this operation.

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Section: Introductionmentioning

confidence: 99%

Composition and product of cover-incomparability graphs

Changat

Anil

2022

Art Discrete Appl. Math.

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“…One possibility is to try to characterize graphs that are cover-incomparability graphs. In [6] it was proved that the recognition problem for cover-incomparability graphs is in general NP-complete. On the other hand there are classes of graphs (such as trees, Ptolemaic graphs, distance-hereditary graphs, block graphs, split graphs or k-trees) for which the recognition problem can be solved in linear time (see [2,3,7,8] for details and proofs).…”

Section: Introductionmentioning

confidence: 99%

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confidence: 98%

Characterizing Subclasses of Cover-Incomparability Graphs by Forbidden Subposets

Bok¹,

Maxová²

2018

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In this paper we continue investigations of cover-incomparability graphs of finite partially ordered sets (see [1,2,3,4] and [6,7]). We consider in some detail the distinction between cover-preserving subsets and isometric subsets of a partially ordered set. This is critical to understanding why forbidden subposet characterizations of certain classes of cover-incomparability graphs in [1] and [3] are not valid as presented.Here we provide examples, investigate the root of the difficulties, and formulate and prove valid revisions of these characterizations.

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“…covering, comparability and incomparability graph). In the paper that followed [8], it was shown that the complexity of recognizing whether a given graph is the C-I graph of some poset is in general NP-complete. In [1] the problem was investigated for the classes of split graphs and block graphs, and the C-I graphs within these two classes of graphs were characterized.…”

Section: Introductionmentioning

confidence: 99%