Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
Finding skew partitions efficiently
Journal of Algorithms
SIAM Journal on Discrete Mathematics
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The list partition problem for graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Parameterized Complexity
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
On the adaptable chromatic number of graphs
European Journal of Combinatorics
An upper bound on adaptable choosability of graphs
European Journal of Combinatorics
Advances on the list stubborn problem
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Dichotomy for tree-structured trigraph list homomorphism problems
Discrete Applied Mathematics
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Algorithms for some h-join decompositions
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Graph partitions with prescribed patterns
European Journal of Combinatorics
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List matrix partitions are restricted binary list constraint satisfaction problems which generalize list homomorphisms and many graph partition problems arising, e.g., in the study of perfect graphs. Most of the existing algorithms apply to concrete small matrices, i.e., to partitions into a small number of parts. We focus on two general classes of partition problems, provide algorithms for their solution, and discuss their implications.The first is an O(nr+2)-algorithm for the list M-partition problem where M is any r by r matrix over subsets of {0, 1}, which has the "bisplit property". This algorithm can be applied to recognize so-called k-bisplit graphs in polynomial time, yielding a solution of an open problem from [2].The second is an algorithm running in time (rn)O(log r log n/log log n)nO(log2r) for the list M-partition problem where M is any r × r matrix over subsets of {0,1,...,q- 1}, with the "incomplete property". This algorithm applies to all non-NP-complete list M-partition problems with r = 3, and it improves the running time of the quasi-polynomial algorithm for the "stubborn problem" from [5], and for the "edge-free three-coloring problem" from [12].