Introduction to algorithms
On the complexity of H-coloring
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
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
Connected and Loosely Connected List Homomorphisms
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
SIAM Journal on Discrete Mathematics
Compaction, Retraction, and Constraint Satisfaction
SIAM Journal on Computing
Computational complexity of compaction to irreflexive cycles
Journal of Computer and System Sciences
Journal of Computer and System Sciences
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
Graph partitions with prescribed patterns
European Journal of Combinatorics
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The compaction problem is to partition the vertices of an input graph G onto the vertices of a fixed target graph H, such that adjacent vertices of G remain adjacent in H, and every vertex and nonloop edge of H is covered by some vertex and edge of G respectively, i.e., the partition is a homomorphism of G onto H (except the loop edges). Various computational complexity results, including both NPcompleteness and polynomial time solvability, have been presented earlier for this problem for various class of target graphs H. In this paper, we pay attention to the input graphs G, and present polynomial time algorithms for the problem for some class of input graphs, keeping the target graph H general as any reflexive or irreflexive graph. Our algorithms also give insight as for which instances of the input graphs, the problem could possibly be NP-complete for certain target graphs. With the help of our results, we are able to further refine the structure of the input graph that would be necessary for the problem to be possibly NP-complete, when the target graph is a cycle. Thus, when the target graph is a cycle, we enhance the class of input graphs for which the problem is polynomial time solvable.