Two algorithms for general list matrix partitions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
(p, k)-coloring problems in line graphs
Theoretical Computer Science
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
On the adaptable chromatic number of graphs
European Journal of Combinatorics
On stable cutsets in claw-free graphs and planar graphs
Journal of Discrete Algorithms
Discrete Applied Mathematics
An upper bound on adaptable choosability of graphs
European Journal of Combinatorics
Parameterizing Cut Sets in a Graph by the Number of Their Components
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
A forbidden subgraph characterization of line-polar bipartite graphs
Discrete Applied Mathematics
The polynomial dichotomy for three nonempty part sandwich problems
Discrete Applied Mathematics
Advances on the list stubborn problem
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Discrete Applied Mathematics
The external constraint 4 nonempty part sandwich problem
Discrete Applied Mathematics
Dichotomy for tree-structured trigraph list homomorphism problems
Discrete Applied Mathematics
Algorithms for partition of some class of graphs under compaction
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Parameterizing cut sets in a graph by the number of their components
Theoretical Computer Science
The computational complexity of disconnected cut and 2K2-partition
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Locally injective graph homomorphism: lists guarantee dichotomy
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Adapted game colouring of graphs
European Journal of Combinatorics
On stable cutsets in claw-free graphs and planar graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Two fixed-parameter algorithms for the cocoloring problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Partitioning cographs into cliques and stable sets
Discrete Optimization
Dense and sparse graph partition
Discrete Applied Mathematics
2K2-partition of some classes of graphs
Discrete Applied Mathematics
The P versus NP-complete dichotomy of some challenging problems in graph theory
Discrete Applied Mathematics
Proceedings of the Winter Simulation Conference
Graph partitions with prescribed patterns
European Journal of Combinatorics
Fixed-parameter algorithms for the cocoloring problem
Discrete Applied Mathematics
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List partitions generalize list colorings and list homomorphisms. (We argue that they may be called list "semihomomorphisms.") Each symmetric matrix M over 0,1,* defines a list partition problem. Different choices of the matrix M lead to many well-known graph theoretic problems, often related to graph perfection, including the problem of recognizing split graphs, finding homogeneous sets, clique cutsets, stable cutsets, and so on. The recent proof of the strong perfect graph theorem employs three kinds of decompositions that can be viewed as list partitions. We develop tools which allow us to classify the complexity of many list partition problems and, in particular, yield the complete classification for small matrices M. Along the way, we obtain a variety of specific results, including generalizations of Lovász's communication bound on the number of clique-versus-stable-set separators, polynomial time algorithms to recognize generalized split graphs, a polynomial algorithm for the list version of the clique cutset problem, and the first subexponential algorithm for the skew cutset problem of Chvátal. We also show that the dichotomy (NP-complete versus polynomial time solvable), conjectured for certain graph homomorphism problems, would, if true, imply a slightly weaker dichotomy (NP-complete versus quasi-polynomial) for our list partition problems.