Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The complexity of some problems related to Graph 3-COLORABILITY
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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Discrete Applied Mathematics
Two algorithms for general list matrix partitions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
List matrix partitions of chordal graphs
Theoretical Computer Science - Graph colorings
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
The polynomial dichotomy for three nonempty part sandwich problems
Discrete Applied Mathematics
Parallelizing a new algorithm for the set partition problem
Annales UMCS, Informatica
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Hi-index | 0.00 |
We consider the problem of partitioning the vertex-set of a graph into at most k parts A1, A2,..., Ak, where it may be specified that Ai induce a stable set, a clique, or an arbitrary subgraph, and pairs Ai, Aj (i ≠ j) be completely non-adjacent, completely adjacent, or arbitrarily adjacent. This problem is generalized to the list version which specifies for each vertex a list of parts in which the vertex is allowed to be placed. Many well-known graph problems can be formulated as list partition problems: e.g. 3-colourability, clique cutset, stable cutset, homogeneous set, skew partition, and 2-clique cutset. We classify, with the exception of two polynomially equivalent problems, each list partition problem with k = 4 as either solvable in polynomial time or NP-complete. In doing so, we provide polynomial-time algorithms for many problems whose polynomial-time solvability was open, including the list 2-clique cutset problem. This also allows us to classify each list generalized 2-clique cutset problem and list generalized skew partition problem as solvable in polynomial time or NP-complete.