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Discrete Applied Mathematics, ISSN 0166-218X, 03/2019, Volume 257, pp. 361 - 367
A vertex or edge in a graph is critical if its deletion reduces the chromatic number of the graph by one. We consider the problems of deciding whether a graph... 
Edge contraction | Vertex deletion | Chromatic number | MATHEMATICS, APPLIED | Deletion | Graphs | Graph theory | Apexes | Complexity | Mathematics | Combinatorics | Data Structures and Algorithms | Computer Science | Discrete Mathematics
Journal Article
Acta Informatica, ISSN 0001-5903, 11/2019, Volume 56, Issue 7, pp. 619 - 648
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 9224, pp. 16 - 300
Conference Proceeding
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
Journal Article
Algorithmica, ISSN 0178-4617, 01/2020, Volume 82, Issue 1, pp. 20 - 40
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 02/2016, Volume 200, pp. 43 - 51
Let  G be a bipartite graph, and let  H be a bipartite graph with a fixed bipartition (BH,WH). We consider three different, natural ways of forbidding  H as an... 
Graph class | Bipartite graph | Clique-width | LINEAR-TIME | MATHEMATICS, APPLIED | SET | CO-GEM-FREE | (P-5,GEM)-FREE GRAPHS | FORBIDDEN SUBGRAPHS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 09/2017, Volume 86, Issue 1, pp. 42 - 77
A graph is H‐free if it has no induced subgraph isomorphic to H. Brandstädt, Engelfriet, Le, and Lozin proved that the class of chordal graphs with... 
forbidden induced subgraph | chordal graph | hereditary graph class | clique‐width | clique-width | MATHEMATICS | CO-GEM-FREE | WEIGHT STABLE SET | PARTITIONING PROBLEMS | ALGORITHMS | SPLIT | TRIANGLE-FREE GRAPHS
Journal Article
Theory of Computing Systems, ISSN 1432-4350, 8/2018, Volume 62, Issue 6, pp. 1409 - 1426
A graph H is a square root of a graph G, or equivalently, G is the square of H, if G can be obtained from H by adding an edge between any two vertices in H... 
Theory of Computation | Clique number | Square root | Computer Science | Cactus | Treewidth | MATHEMATICS | SQUARE ROOTS | COMPUTER SCIENCE, THEORY & METHODS | SPLIT GRAPHS | Computer science | Computational mathematics | Graph theory | Polynomials | Algorithms
Journal Article
Journal of Computer and System Sciences, ISSN 0022-0000, 09/2019, Volume 104, pp. 202 - 215
We continue the study into the clique-width of graph classes defined by two forbidden induced graphs. We present three new classes of bounded clique-width and... 
Graph class | Forbidden induced subgraphs | Clique-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | SET | CO-GEM-FREE | COMPUTER SCIENCE, THEORY & METHODS | TRIANGLE-FREE GRAPHS | BIPARTITE GRAPHS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 08/2017, Volume 689, pp. 36 - 47
A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are at distance 2 from each... 
Square root | k-apex graphs | Linear kernel | COMPUTER SCIENCE, THEORY & METHODS | SPLIT
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2017, Volume 84, Issue 4, pp. 331 - 363
For a positive integer k, a k‐coloring of a graph G=(V,E) is a mapping c:V→{1,2,...,k} such that c(u)≠c(v) whenever uv∈E. The Coloring problem is to decide,... 
precoloring extension | graph coloring | forbidden induced subgraph | list coloring | choosability | CHROMATIC NUMBER | CLAW-FREE GRAPHS | TRIANGLE-FREE GRAPHS | NP-COMPLETENESS | MATHEMATICS | UPPER-BOUNDS | 3-COLORABILITY | K-COLORABILITY | ABSENCE | VERTICES | INDEX
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 08/2017, Volume 61, pp. 309 - 315
Testing if a given graph G contains the k-vertex path Pk as a minor or as an induced minor is trivial for every fixed integer k≥1. The situation changes for... 
edge contraction | bipartite graph | path
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2019, Volume 257, pp. 361 - 367
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
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 12/2016, Volume 83, Issue 4, pp. 340 - 358
Let G be a simple undirected connected graph on n vertices with maximum degree Δ. Brooks' Theorem states that G has a proper Δ‐coloring unless G is a complete... 
reconfigurations | Brooks’ Theorem | graph coloring | LIST EDGE-COLORINGS | GRAPH | MATHEMATICS | Brooks' Theorem | COMPLEXITY
Journal Article
Games and Economic Behavior, ISSN 0899-8256, 03/2018, Volume 108, pp. 245 - 268
We consider multiple partners matching games (G,b,w), where G is a graph with an integer vertex capacity function b and an edge weighting w. If G is bipartite,... 
Stable solutions | Cooperative game | Core | Economics and Econometrics | Finance | GAMES | COMPLEXITY | ASSIGNMENT | ECONOMICS
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 1/2014, Volume 27, Issue 1, pp. 132 - 143
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
Theoretical Computer Science, ISSN 0304-3975, 2012, Volume 414, Issue 1, pp. 9 - 19
A graph is H -free if it does not contain an induced subgraph isomorphic to the graph H . The graph P k denotes a path on k vertices. The ℓ - Coloring problem... 
Linear forest | Forbidden induced subgraph | Graph coloring | METIS-293161 | MSC-05C | EWI-21077 | IR-82685 | COMPUTER SCIENCE, THEORY & METHODS | 3-COLORABILITY | ALGORITHM | Coloring | Forests | Reproduction | Classification | Graphs | Unions | Complexity
Journal Article
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