Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 501 - 511

The class of cographs is known to have unbounded linear clique‐width. We prove that a hereditary class of cographs has bounded linear clique‐width if and only...

linear clique‐width | threshold graphs | quasi‐threshold graphs | clique‐width | cographs | clique-width | quasi-threshold graphs | linear clique-width | MATHEMATICS | NLC-WIDTH | GRAPHS

linear clique‐width | threshold graphs | quasi‐threshold graphs | clique‐width | cographs | clique-width | quasi-threshold graphs | linear clique-width | MATHEMATICS | NLC-WIDTH | GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 248, pp. 145 - 152

The celebrated theorem of Robertson and Seymour states that in the family of minor-closed graph classes, there is a unique minimal class of graphs of unbounded...

Hereditary class | Linear clique-width | Clique-width | MINORS | MATHEMATICS, APPLIED

Hereditary class | Linear clique-width | Clique-width | MINORS | MATHEMATICS, APPLIED

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 187, pp. 70 - 81

Clique-width of graphs is defined algebraically through operations on graphs with vertex labels. We characterise the clique-width in a combinatorial way by...

Efficient representation | Linear clique-width | Characterisation | Clique-width | MATHEMATICS, APPLIED | GRAPHS | Logic in Computer Science | Computer Science

Efficient representation | Linear clique-width | Characterisation | Clique-width | MATHEMATICS, APPLIED | GRAPHS | Logic in Computer Science | Computer Science

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2015, Volume 9079, pp. 167 - 181

Conference Proceeding

SIAM journal on computing, ISSN 1095-7111, 2008, Volume 38, Issue 3, pp. 1012 - 1032

We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input...

Graph | Rank-width | Matroid | Fixed-parameter tractable algorithm | Branch-width | Clique-width | MATHEMATICS, APPLIED | branch-width | rank-width | RECOGNITION | fixed-parameter tractable algorithm | VERTEX-MINORS | ALGORITHMS | FIXED CLIQUE-WIDTH | graph | GRAPHS | clique-width | MATROIDS | MONADIC 2ND-ORDER LOGIC | COMPUTER SCIENCE, THEORY & METHODS | matroid

Graph | Rank-width | Matroid | Fixed-parameter tractable algorithm | Branch-width | Clique-width | MATHEMATICS, APPLIED | branch-width | rank-width | RECOGNITION | fixed-parameter tractable algorithm | VERTEX-MINORS | ALGORITHMS | FIXED CLIQUE-WIDTH | graph | GRAPHS | clique-width | MATROIDS | MONADIC 2ND-ORDER LOGIC | COMPUTER SCIENCE, THEORY & METHODS | matroid

Journal Article

Journal of Computer and System Sciences, ISSN 0022-0000, 11/2017, Volume 89, pp. 410 - 431

The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we...

Forbidden induced subgraph | Graph colouring | Diamond-free | Clique-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | CO-GEM-FREE | TRIANGLE-FREE GRAPHS | LINEAR-TIME | BOUNDED CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | HEREDITARY CLASSES | FORBIDDEN SUBGRAPHS | BIPARTITE GRAPHS | Logic | Mathematics

Forbidden induced subgraph | Graph colouring | Diamond-free | Clique-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | CO-GEM-FREE | TRIANGLE-FREE GRAPHS | LINEAR-TIME | BOUNDED CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | HEREDITARY CLASSES | FORBIDDEN SUBGRAPHS | BIPARTITE GRAPHS | Logic | Mathematics

Journal Article

ACM Transactions on Computational Logic (TOCL), ISSN 1529-3785, 07/2015, Volume 16, Issue 3, pp. 1 - 27

Clique-width is a graph invariant that has been widely studied in combinatorics and computational logic. Computing the clique-width of a graph is an intricate...

k-expression | satisfiability | linear clique-width | SAT solver | SAT encoding | Clique-width | cardinality constraint | K-expression | Linear clique-width | Cardinality constraint | Satisfiability | Theory | LOGIC | GRAPHS | Algorithms | Experimentation | COMPUTER SCIENCE, THEORY & METHODS

k-expression | satisfiability | linear clique-width | SAT solver | SAT encoding | Clique-width | cardinality constraint | K-expression | Linear clique-width | Cardinality constraint | Satisfiability | Theory | LOGIC | GRAPHS | Algorithms | Experimentation | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Graphs and combinatorics, ISSN 1435-5914, 2019, Volume 36, Issue 1, pp. 125 - 138

A hole is a chordless cycle with at least four vertices. A hole is even if its number of vertices is even. Given a set L of graphs, a graph G is L-free if G...

MATHEMATICS | CLIQUE-WIDTH | Graph coloring | Perfect graphs | GRAPHS | Coloring | Graphs | Graph theory | Apexes | Complexity

MATHEMATICS | CLIQUE-WIDTH | Graph coloring | Perfect graphs | GRAPHS | Coloring | Graphs | Graph theory | Apexes | Complexity

Journal Article

Journal of Computer and System Sciences, ISSN 0022-0000, 12/2019, Volume 106, pp. 60 - 79

The complexity of Colouring is fully understood for H-free graphs, but there are still major complexity gaps if two induced subgraphs H1 and H2 are forbidden....

Atoms | Graph colouring | Forbidden induced subgraphs | Clique-width | NP-COMPLETENESS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | SET | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Hardness

Atoms | Graph colouring | Forbidden induced subgraphs | Clique-width | NP-COMPLETENESS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | SET | COMPLEXITY | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Hardness

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 248, pp. 68 - 78

We study the parameterized complexity of the classical Edge Hamiltonian Path problem and give several fixed-parameter tractability results. First, we settle...

Structural parameterization | Edge Hamiltonicity | Polynomial kernel | Fixed parameter tractability | EULERIAN SUBGRAPHS | MATHEMATICS, APPLIED | CLIQUE-WIDTH | OPTIMIZATION | PATH PROBLEM | GRAPHS | Computer Science

Structural parameterization | Edge Hamiltonicity | Polynomial kernel | Fixed parameter tractability | EULERIAN SUBGRAPHS | MATHEMATICS, APPLIED | CLIQUE-WIDTH | OPTIMIZATION | PATH PROBLEM | GRAPHS | Computer Science

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 05/2018, Volume 130, pp. 1 - 18

Does well-quasi-ordering by induced subgraphs imply bounded clique-width for hereditary classes? This question was asked by Daligault, Rao, and Thomassé [7]....

Well-quasi-ordering | Hereditary classes | Induced subgraphs | Clique-width | MATHEMATICS | GRAPH MINORS

Well-quasi-ordering | Hereditary classes | Induced subgraphs | Clique-width | MATHEMATICS | GRAPH MINORS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2020, Volume 285, pp. 688 - 690

We prove that (4K1,C4,C5,C7)-free graphs that are not chordal have unbounded clique-width. This disproves a conjecture from Fraser et al. (2017).

Forbidden induced subgraphs | Clique-width

Forbidden induced subgraphs | Clique-width

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2016, Volume 211, pp. 30 - 39

A graph is H-free if it has no induced subgraph isomorphic to H. We continue a study into the boundedness of clique-width of subclasses of perfect graphs. We...

Split graph | Forbidden induced subgraph | Hereditary graph class | Perfect graph | Clique-width | MATHEMATICS, APPLIED | CO-GEM-FREE | (P-5,GEM)-FREE GRAPHS | FORBIDDEN SUBGRAPHS | TRIANGLE-FREE GRAPHS | BIPARTITE GRAPHS

Split graph | Forbidden induced subgraph | Hereditary graph class | Perfect graph | Clique-width | MATHEMATICS, APPLIED | CO-GEM-FREE | (P-5,GEM)-FREE GRAPHS | FORBIDDEN SUBGRAPHS | TRIANGLE-FREE GRAPHS | BIPARTITE GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2016, Volume 199, pp. 16 - 29

Bichain graphs form a bipartite analog of split permutation graphs, also known as split graphs of Dilworth number 2. Unlike graphs of Dilworth number 1 that...

Split permutation graph | Intersection graph | Universal graph | MATHEMATICS, APPLIED | CLIQUE-WIDTH | SUBGRAPHS | SPLIT GRAPHS

Split permutation graph | Intersection graph | Universal graph | MATHEMATICS, APPLIED | CLIQUE-WIDTH | SUBGRAPHS | SPLIT GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 01/2016, Volume 339, Issue 1, pp. 222 - 226

We determine the relationship between the graph parameters neighbourhood-width and path-width of trees, that turn out equivalent. As our main combinatorial...

Neighbourhood-width | Trees | Path-width | MATHEMATICS | NUMBER | VERTEX SEPARATION | CLIQUE-WIDTH | GRAPH MINORS

Neighbourhood-width | Trees | Path-width | MATHEMATICS | NUMBER | VERTEX SEPARATION | CLIQUE-WIDTH | GRAPH MINORS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 12/2015, Volume 197, pp. 53 - 58

We study the computational complexity of the minimum dominating set problem on graphs restricted by forbidden induced subgraphs. We give some dichotomies...

Algorithms | Dominating set | Forbidden induced subgraphs | Complexity | MATHEMATICS, APPLIED | SETS | ALGORITHM | CHORDAL GRAPHS | CLIQUE-WIDTH | BIPARTITE GRAPHS

Algorithms | Dominating set | Forbidden induced subgraphs | Complexity | MATHEMATICS, APPLIED | SETS | ALGORITHM | CHORDAL GRAPHS | CLIQUE-WIDTH | BIPARTITE GRAPHS

Journal Article

Algorithmica, ISSN 0178-4617, 07/2018, Volume 80, Issue 7, pp. 2160 - 2180

The problem MaxW-Light (MaxW-Heavy) for an undirected graph is to assign a direction to each edge so that the number of vertices of outdegree at most W (resp....

Computer Science(all) | Width parameter | Computer Science Applications | Graph class | Orientation | Applied Mathematics | Parameterized complexity | MATHEMATICS, APPLIED | TREEWIDTH | ALGORITHMS | LOGIC | COMPUTER SCIENCE, SOFTWARE ENGINEERING | CLIQUE-WIDTH | VERTICES | SUBGRAPHS | OUT-DEGREE | Computer science | Algorithms

Computer Science(all) | Width parameter | Computer Science Applications | Graph class | Orientation | Applied Mathematics | Parameterized complexity | MATHEMATICS, APPLIED | TREEWIDTH | ALGORITHMS | LOGIC | COMPUTER SCIENCE, SOFTWARE ENGINEERING | CLIQUE-WIDTH | VERTICES | SUBGRAPHS | OUT-DEGREE | Computer science | Algorithms

Journal Article

Journal of the ACM (JACM), ISSN 0004-5411, 10/2012, Volume 59, Issue 5, pp. 1 - 64

We give a logical characterization of the polynomial-time properties of graphs embeddable in some surface. For every surface S , a property P of graphs...

graph isomorphism | graph minors | Descriptive complexity | fixed-point logics | Fixed-point logics | Graph isomorphism | Graph minors | ISOMORPHISM | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | Theory | COMPUTER SCIENCE, INFORMATION SYSTEMS | LOGIC | COMPUTER SCIENCE, SOFTWARE ENGINEERING | QUERIES | Algorithms | COMPLEXITY | CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | PARALLEL

graph isomorphism | graph minors | Descriptive complexity | fixed-point logics | Fixed-point logics | Graph isomorphism | Graph minors | ISOMORPHISM | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | Theory | COMPUTER SCIENCE, INFORMATION SYSTEMS | LOGIC | COMPUTER SCIENCE, SOFTWARE ENGINEERING | QUERIES | Algorithms | COMPLEXITY | CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | PARALLEL

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 07/2019, Volume 15, Issue 3, pp. 1 - 57

Recently, hardness results for problems in P were achieved using reasonable complexity-theoretic assumptions such as the Strong Exponential Time Hypothesis....

split decomposition | neighbourhood diversity | clique-width | primeval decomposition | fully polynomial FPT | modular decomposition | Hardness in P | Fully polynomial FPT | Neighbourhood diversity | Split decomposition | Modular decomposition | Primeval decomposition | Clique-width | MATHEMATICS, APPLIED | RECOGNITION | TREES | THEOREMS | COMPUTER SCIENCE, THEORY & METHODS | O(N) TIME ALGORITHM

split decomposition | neighbourhood diversity | clique-width | primeval decomposition | fully polynomial FPT | modular decomposition | Hardness in P | Fully polynomial FPT | Neighbourhood diversity | Split decomposition | Modular decomposition | Primeval decomposition | Clique-width | MATHEMATICS, APPLIED | RECOGNITION | TREES | THEOREMS | COMPUTER SCIENCE, THEORY & METHODS | O(N) TIME ALGORITHM

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 04/2015, Volume 185, pp. 138 - 167

Bubble models are 2-dimensional representations of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties....

Proper interval graphs | Characterisation | Forbidden induced subgraphs | Clique-width | Polynomial time | MATHEMATICS, APPLIED | Intervals | Graphs | Bubbles | Mathematical models | Representations

Proper interval graphs | Characterisation | Forbidden induced subgraphs | Clique-width | Polynomial time | MATHEMATICS, APPLIED | Intervals | Graphs | Bubbles | Mathematical models | Representations

Journal Article

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