Absolute retracts of bipartite graphs
Discrete Applied Mathematics
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Absolute reflexive retracts and absolute bipartite retracts
Discrete Applied Mathematics
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
Computational complexity of compaction to cycles
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computational Complexity of Compaction to Reflexive Cycles
SIAM Journal on Computing
Journal of Computer and System Sciences
Mixing 3-colourings in bipartite graphs
European Journal of Combinatorics
Mixing 3-colourings in bipartite graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Algorithms for partition of some class of graphs under compaction
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
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In this paper, we solve a long-standing problem that has been of interest since about 1988. The problem in general is to decide whether or not it is possible to partition the vertices of a graph into k distinct non-empty sets A0, A1,..., Ak-1, such that the vertices in Ai, are independent and there is at least one edge between the pair of sets Ai, and A(i+1) mod k, for all i = 0, 1, 2,..., k - 1, k 2, and there is no edge between any other pair of sets. Determining the computational complexity of this problem, for any value of even k ≥ 6. has been of interest since about 1988 to various people, including Pavol Hell and Jaroslav Nesetril. We show in this paper that the problem is NP-complete, for all even k ≥ 6. We study the problem as the compaction problem for an irreflexive k-cycle.