Abstract
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 26 December 2018Accepted: 03 February 2020Published online: 05 May 2020Keywordsclique-width, hereditary graph class, dichotomyAMS Subject Headings05C78, 05C75, 05C69Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied MathematicsCODEN: sjdmec
Highlights
Many graph-theoretic problems that are computationally hard for general graphs may still be solvable in polynomial time if the input graph can be decomposed into large parts of “Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany73:2 Clique-Width for Graph Classes Closed under Complementation behaving” vertices
No polynomial-time algorithms are known for computing the clique-width of very restricted graph classes, such as unit interval graphs, or for deciding whether a graph has clique-width at most 4.1 In order to get a better understanding of clique-width and to identify new “islands of tractability” for central NP-hard problems, many graph classes of bounded and unbounded clique-width have been identified; see, for instance, the Information System on Graph Classes and their Inclusions [24], which keeps a record of such graph classes
In this paper we study the following research question: What kinds of properties of a graph class ensure that its clique-width is bounded?
Summary
Many graph-theoretic problems that are computationally hard for general graphs may still be solvable in polynomial time if the input graph can be decomposed into large parts of “. In the same section we combine this new result with known results to prove the following theorem, which, together with Theorem 1, shows to what extent the property of being closed under complementation helps with bounding the clique-width for bigenic graph classes (see Figure 1). By combining this with known results, we discovered that the classification of boundedness of clique-width for (H, H, C5)-free graphs coincides with the one of Theorem 2 This raised the question of whether the same is true for other sets of self-complementary graphs F = {C5}. Another consequence of our result for (2P1 + P3, 2P1 + P3)-free graphs is that Colouring is polynomial-time solvable for this graph class This result was used by Blanché et al [2]: Theorem 5 ([2]).
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