Computing vertex-surjective homomorphisms to partially reflexive trees
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
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Discrete Applied Mathematics
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
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ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Graph partitions with prescribed patterns
European Journal of Combinatorics
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For a fixed graph $H$, let $\textsc{Ret}(H)$ denote the problem of deciding whether a given input graph is retractable to $H$. We classify the complexity of $\textsc{Ret}(H)$ when $H$ is a graph (with loops allowed) where each connected component has at most one cycle, i.e., a pseudoforest. In particular, this result extends the known complexity classifications of $\textsc{Ret}(H)$ for reflexive and irreflexive cycles to general cycles. Our approach is based mainly on algebraic techniques from universal algebra that previously have been used for analyzing the complexity of constraint satisfaction problems.