Parameterizing Cut Sets in a Graph by the Number of Their Components
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Advances on the list stubborn problem
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
The external constraint 4 nonempty part sandwich problem
Discrete Applied Mathematics
Dichotomy for tree-structured trigraph list homomorphism problems
Discrete Applied Mathematics
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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
The P versus NP-complete dichotomy of some challenging problems in graph theory
Discrete Applied Mathematics
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Graph partitions with prescribed patterns
European Journal of Combinatorics
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The $k$-partition problem is as follows: Given a graph $G$ and a positive integer $k$, partition the vertices of $G$ into at most $k$ parts $A_1, A_2, \ldots , A_k$, where it may be specified that $A_i$ induces a stable set, a clique, or an arbitrary subgraph, and pairs $A_i, A_j (i \neq j)$ be completely nonadjacent, completely adjacent, or arbitrarily adjacent. The list $k$-partition problem generalizes the $k$-partition problem by specifying for each vertex $x$, a list $L(x)$ of parts in which it is allowed to be placed. Many well-known graph problems can be formulated as list $k$-partition problems: e.g., 3-colorability, clique cutset, stable cutset, homogeneous set, skew partition, and 2-clique cutset. We classify, with the exception of two polynomially equivalent problems, each list 4-partition problem 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.