The chromatic index of complete multipartite graphs
Journal of Graph Theory
Clique Graphs of Chordal and Path Graphs
SIAM Journal on Discrete Mathematics
Journal of Algorithms
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
On edge-colouring indifference graphs
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Discrete Mathematics
Classifications and characterizations of snarks
Discrete Mathematics
Characterizing and edge-colouring split-indifference graphs
Discrete Applied Mathematics
The homogeneous set sandwich problem
Information Processing Letters
The complexity of some problems related to Graph 3-COLORABILITY
Discrete Applied Mathematics
Discrete Applied Mathematics
Finding skew partitions efficiently
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The graph sandwich problem for 1-join composition is NP-complete
Discrete Applied Mathematics
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
SIAM Journal on Discrete Mathematics
Vertex Colouring and Forbidden Subgraphs – A Survey
Graphs and Combinatorics
Cliques and extended triangles. A necessary condition for planar clique graphs
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Distances and diameters on iterated clique graphs
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
On decision and optimization (k, l)-graph sandwich problems
Discrete Applied Mathematics
Combinatorica
Theoretical Computer Science
The sandwich problem for cutsets: clique cutset, k-star cutset
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
Theoretical Computer Science
Edge-colouring of regular graphs of large degree
Theoretical Computer Science
Skew partitions in perfect graphs
Discrete Applied Mathematics
The Complexity of the List Partition Problem for Graphs
SIAM Journal on Discrete Mathematics
Clique-inverse graphs of K3-free and K4-free graphs
Journal of Graph Theory
Journal of Graph Theory
Fast Skew Partition Recognition
Computational Geometry and Graph Theory
The complexity of clique graph recognition
Theoretical Computer Science
The status of the P versus NP problem
Communications of the ACM - The Status of the P versus NP Problem
A structure theorem for graphs with no cycle with a unique chord and its consequences
Journal of Graph Theory
Chromatic index of graphs with no cycle with a unique chord
Theoretical Computer Science
The polynomial dichotomy for three nonempty part sandwich problems
Discrete Applied Mathematics
The external constraint 4 nonempty part sandwich problem
Discrete Applied Mathematics
The computational complexity of disconnected cut and 2K2-partition
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Graph partitions with prescribed patterns
European Journal of Combinatorics
Theoretical Computer Science
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The Clay Mathematics Institute has selected seven Millennium Problems to motivate research on important classic questions that have resisted solution over the years. Among them is the central problem in theoretical computer science: the P versus NP problem, which aims to classify the possible existence of efficient solutions to combinatorial and optimization problems. The main goal is to determine whether there are questions whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. In this context, it is important to determine precisely what facet of a problem makes it NP-complete. We shall discuss classes of problems for which dichotomy results do exist: every problem in the class is classified into polynomial or NP-complete. We shall discuss our contribution through the classification of some long-standing problems in important areas of graph theory: perfect graphs, intersection graphs, and structural characterization of graph classes. More precisely, we have shown that Chvatal's skew partition is polynomial and that Roberts-Spencer's clique graph is NP-complete. We have also solved the dichotomy for Golumbic-Kaplan-Shamir's sandwich problem. We shall describe two examples where we can determine the full dichotomy: the edge-colouring problem for graphs with no cycle with a unique chord and the three nonempty part sandwich problem. Some open problems are discussed: the stubborn problem for list partition, the chromatic index of chordal graphs, and the recognition of split clique graphs.