Clique-width and well-quasi-ordering of triangle-free graph classes

Dabrowski, Konrad K.; Paulusma, Daniël

doi:10.1016/j.jcss.2019.09.001

Cited by 8 publications

(3 citation statements)

References 38 publications

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“…Such graph classes are said to be hereditary and there is a long‐standing study on the boundedness of clique‐width for hereditary graph classes (see e.g. [3, 6, 8, 9, 12–15, 28, 30, 32, 33, 35, 36, 45, 51, 57]).…”

Section: Introductionmentioning

confidence: 99%

Clique‐width: Harnessing the power of atoms

Dabrowski

Masařík

Novotná

et al. 2023

Journal of Graph Theory

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Many NP‐complete graph problems are polynomial‐time solvable on graph classes of bounded clique‐width. Several of these problems are polynomial‐time solvable on a hereditary graph class if they are so on the atoms (graphs with no clique cut‐set) of . Hence, we initiate a systematic study into boundedness of clique‐width of atoms of hereditary graph classes. A graph is ‐free if is not an induced subgraph of , and it is ‐free if it is both ‐free and ‐free. A class of ‐free graphs has bounded clique‐width if and only if its atoms have this property. This is no longer true for ‐free graphs, as evidenced by one known example. We prove the existence of another such pair and classify the boundedness of clique‐width on ‐free atoms for all but 18 cases.

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Section: Introductionmentioning

confidence: 99%

Clique‐width: Harnessing the power of atoms

Dabrowski

Masařík

Novotná

et al. 2023

Journal of Graph Theory

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show abstract

“…The type of graph classes we consider all have the natural property that they are closed under vertex deletion. Such graph classes are said to be hereditary and there is a long-standing study on boundedness of clique-width for hereditary graph classes (see, for example, [3,6,7,8,10,11,12,13,24,25,27,28,30,31,39,45,48]).…”

Section: Introductionmentioning

confidence: 99%

Clique-Width: Harnessing the Power of Atoms

Dabrowski

Masařík

Novotná

et al. 2020

Graph-Theoretic Concepts in Computer Science

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Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of G. Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph G is H-free if H is not an induced subgraph of G, and it is (H1, H2)-free if it is both H1-free and H2-free. A class of H-free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for (H1, H2)-free graphs, as evidenced by one known example. We prove the existence of another such pair (H1, H2) and classify the boundedness of clique-width on (H1, H2)-free atoms for all but 18 cases.

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“…The type of graph classes we consider all have the natural property that they are closed under vertex deletion. Such graph classes are said to be hereditary and there is a long-standing study on boundedness of clique-width for hereditary graph classes (see, for example, [3,6,8,9,12,13,14,15,26,28,30,31,32,33,41,47,53]).…”

Section: Introductionmentioning

confidence: 99%

Clique-Width: Harnessing the Power of Atoms

Dabrowski¹,

Masařík²,

Novotná³

et al. 2020

Preprint

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Many NP-complete graph problems are polynomially solvable on graph classes of bounded clique-width. Several of these problems are polynomially solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of G. Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph G is H-free if H is not an induced subgraph of G, and G is (H1, H2)-free if it is both H1-free and H2-free. A class of H-free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for (H1, H2)-free graphs as evidenced by one known example. We prove the existence of another such pair (H1, H2) and classify the boundedness of (H1, H2)-free atoms for all but 22 cases.

show abstract

Clique-width and well-quasi-ordering of triangle-free graph classes

Cited by 8 publications

References 38 publications

Clique‐width: Harnessing the power of atoms

Clique‐width: Harnessing the power of atoms

Clique-Width: Harnessing the Power of Atoms

Clique-Width: Harnessing the Power of Atoms

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